7. Suppose that you are dealt a hand of 9 cards from a standard deck of 52 playing cards.

a. What is the probability that you are dealt exactly 3 kings?

b. What is the probability that you are dealt 9 cards of the same suit?

c. What is the probability that you are not dealt at least 2 cards of each suit?

11. In how many ways can the letters in the word POSSESSIONS be arranged?

a. In how many ways can they be arranged if the first letter must be an S and the last letter must be an E?

88. Refer to the Baseball 2005 data, which reports information on the 30 major league teams

for the 2005 baseball season.

a. Select the variable team salary and find the mean, median, and the standard deviation.

b. Select the variable that refers to the age the stadium was built. (Hint: Subtract the

year in which the stadium was built from the current year to find the stadium age and

work with that variable.) Find the mean, median, and the standard deviation.

c. Select the variable that refers to the seating capacity of the stadium. Find the mean,

median, and the standard deviation.

56. Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of

the scheduled time is .90. We select four flights from yesterday for study.

a. What is the likelihood all four of the selected flights arrived within 15 minutes of the

scheduled time?

b. What is the likelihood that none of the selected flights arrived within 15 minutes of

the scheduled time?

c. What is the likelihood at least one of the selected flights did not arrive within 15 minutes

of the scheduled time?

64. An internal study by the Technology Services department at Lahey Electronics revealed

company employees receive an average of two emails per hour. Assume the arrival of

these emails is approximated by the Poisson distribution.

a. What is the probability Linda Lahey, company president, received exactly 1 email

between 4 P.M. and 5 P.M. yesterday?

b. What is the probability she received 5 or more email during the same period?

c. What is the probability she did not receive any email during the period?

A survey of a group’s viewing habits over the last year revealed the following information:

1. 28% watched gymnastics

2. 29% watched baseball

3. 19% watched soccer

4. 14% watched gymnastics and baseball

5. 12% watched baseball and soccer

6. 10% watched gymnastics and soccer

7. 8% watched all three sports

Calculate the percentage of the group that watched none of the three sports during last year.

1. A cooler contains 100 cans of soda covered by ice. There are 30 cans of cola, 40 cans of orange soda, 10 cans of ginger ale, and 20 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the cooler, determine the probability that the soda selected will be cola or orange.

2. Brain Teaser. A multiple- choice exam has four possible answers. For each correct answer you are awarded 5 points. For each incorrect answer 2 points are taken away from your score. For answers left blank no points are added or subtracted.

a) If you do not know the correct answer to a particular question, is it to your advantage to guess? Please explain your answer.

b)If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Please explain your answer.

3. Answer the following question. If a wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on a number greater than 6 given that the color is red. Hint. There are 3 red colors on the wheel with numbers 5,6,7. 2 green colors on the wheel with numbers 1,8. 5 purple colors on the wheel with numbers 2,4,9,11,12 and 2 brown colors on the wheel with numbers 3,10.

A committee of four is to be randomly selected from a group of seven teachers and eight students. Find the probability that the committee will consist of four students.

Secured doors at airports and other locations are opened by pressing the correct sequence of numbers on a control panel. If the correct panel contains the digits 0-9 and three digit code must be entered (repetition is permitted)

a) How many different codes are possible?

b) If one code is entered at random, find the probability the correct code is entered.

If the annual proportion of erroneous income tax returns filed with the IRS can be looked upon as a random variable having a beta distribution with α= 2 and β = 9, what is the probability that in any given year there will be fewer than 10 percent erroneous returns

It has been recorded that the average number of errors in a newspaper is 4 mistakes per page. What is the probability of having 0 or one error per page?

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a

fatality. Over a lifetime, an average U.S. driver takes 50,000 trips.

(a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully.

(b) Why might a driver be tempted not to use a seat belt “just on this trip”?

A cola-dispensing machine is set to dispense 9.00 ounces of cola per cup, with a standard deviation of 1.00 ounces. The manufacturer of the machine would like to set the control limit in such a way that for samples of 36,5 percent of the sample means will be greater than the upper control limits, and 5 percent of the sample mean will be less than the lower control limit.

a. At what value should the control limit be set?

b. What is the probability that if the population mean shifts to 8.9, this change will not be detected?

c. What is the probability that if the population mean shifts to 9.3, this change will not be detected?

The ratings for “driving distance off the tee” for the top 10 golfers on the PGA Tour are as follows:

RANK PREV RANK PLAYER VALUE (YDS)

1 1 Scott Hend 318.90

2 2 Tiger Woods 315.20

3 3 Brett Wetterich 310.70

4 4 John Daly 308.50

5 6 Scott Gutschewski 308.40

6 5 Hank Kuehne 308.30

7 10 Davis Love III 304.30

How would you compute the probability, for any given drive on any given hole in any given tournament of the following probabilities for Tiger Woods, currently rated the Number One player in the world:

Note: Let D = the event “a given drive”

I am NOT looking for specific probability numbers – I want to know how

you would compute them and what additional data you might need to

make the computation using the methodology you suggest.

a) P(D = 310 yards) = ? How would you determine this probability? What assumptions did you make?

b) P(300 < D < 320) = ? How would you determine this probability? What

assumptions did you make?

c) P(300 < D < 320) = ? How would you determine this probability? What assumptions did you make?

In humans, the ability to taste PTC is inherited as a dominant gene (T; Taster). in a marriage between two heterozygous tasters (Tt):

a) what is the probability of 3 taster children?

b)what is the probability of 3 taster girls?

c)if they have 5 children, what is the probability that the first 3 will be tasters and the last 2 nontasters?

d)how many different ways could they have 3 taster and 2 nontaster children in any order?

e)what is the probabilty that they will have 3 taster and 2 nontaster children in any order?

Let P(X) =.55 and P(Y) = .35. Assume the probability that they both occur is .20. What is the probability of either X or Y occurring?

A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

a. What is the probability a vacationer will visit at least one of these attractions?

b. What is the probability .35 called?

c. Are the events mutually exclusive? Explain.

The human resource director of Sunshine Corporation uses a paper-pencil test that measures work habits to help decide whom to hire. From her past research with the company, she has found the correlation-for those who are hired-between the work-habits inventory and a job performance scale after one year to be +.80. She decides to use the work-habits inventory as a selection device for hiring. The mean of the work-habits inventory = 25, standard deviation (SD) = 6; for job performance, the mean = 5 and the SD = 1.8.

1) Trina, a prospective employee, receives a score of 27 on the work-habits inventory. What is her predicted job performance scale score?

2) Rolando, another prospective employee, ‘receives a score of 14 on the work-habits inventory.

What is his predicted job performance scale score?

3) If we assume that the work-habits inventory scores are normally distributed, what is the probability that someone would score 10 or lower?

4) You have a friend who is conducting a research study and wants to make sure that the religious affiliation of her sample is representative of the population she is interested in studying. What type of sampling technique would you suggest she use, and why?

5) You are extremely bored one night and decide to go to the Isle of Capri Casino in Boonville, Missouri, for fun (you’re really bored) You decide to play some roulette but are only going to bet on “red” or “black” (you’re betting that the marble will land on either a red or black number) After betting on black six times in a row and losing six times in a row, you’re convinced that the odds are in your favor that the next spin will result in black winning. Please describe the error in your thinking.

6) You and three friends are all taking the same statistics course. Assuming that each of you has a probability of .75 of getting an A in the course, what is the probability that all four of you . will get As (assuming that the probability of each one of you getting an A is independent of each other)’!

7) You and another friend are taking a math course together, and the probability that you will get an A is.80, but your friend’s probability is only .45. What is the probability that either one of you will get an A?

The probability

——————————————————————————–

1) A very rich investor has a small amount of spare cash which she wishes to invest. She has four options to choose from. She thinks company 1 has a 43% chance of giving her a return of $327, otherwise she believes it will lose her $296. She thinks company 2 has a 81% chance of giving her a return of $228, otherwise she believes it will lose her $1043. She thinks company 3 has a 46% chance of giving her a return of $181, otherwise she believes it will lose her $187. She thinks company 4 has a 33% chance of giving her a return of $705, otherwise she believes it will lose her $205. Based on these opinions, which company should she invest in?

2) In a certain mining town there are 3 times as many men as women. 64% of the men and 28% of the women attend the weekly football match. During half time a ticket is selected and the holder of that ticket is selected to win a prize. What is the probability that the holder of the winning ticket is a woman?

1. Suppose that for a 5-year-old automobile, the probability the engine will need repair in year 6 is 0.3, while the probability that the tires need replacing in year 6 is 0.8. The probability that both the engine will need repair and the tires will need replacing in year 6 is 0.2. What is the probability that the tires will need to be replaced and the engine will need repair?

ANSWER AND EXPLANATION

2. Suppose that for a 5 year old automobile, the probability the engine will need repair in year 6 is 0.3, while the probability that the tires need replacing in year 6 is 0.8. The probability that both the engine will need repair and the tires will need replacing in year 6 is 0.2. If it is known that the tires will need replacing, what is the probability that the engine needs repair?

ANSWER AND EXPLANATION

1. A survey of 100 MBA students found that 75 owned mutual funds, 45 owned stocks, and 25 owned both.

a. What is the probability that a student owns a stock? A mutual fund?

b. What is the probability that a student owns neither stocks nor mutual funds?

c. What is the probability that a student owns either a stock or mutual fund?

Probability Rules and Calculations

Rule 1. The probability associated with any outcome must be between 0 and 1.

Rule 2. The sum of the probabilities over all possible outcomes must be 1.0.

Rule 3. The probability of any event is the sum of the probabilities of the outcomes that compose that event.

Rule 4. If events A and B are mutually exclusive, then P(Aor B) = P(A) + P(B).

Rule 5. If two events A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B).

Submit your problem set in a single worksheet file. Thanks.

1. A cube has all 6 sides painted blue; this cube is then cut into 64 equal cubes. What is the probability, Pn where n = 1, 2, 3, that a little cube (one of the 64) picked at random will have n painted faces?

2. A person is given 4 coins each with equal and independent probabilities of being a nickel , a penny, a dime or a quarter. What is the probability the person has been 37 cents

Please give a complete answer with explanations.

According to the “January theory,” if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 28 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5.

What is the probability this could occur by chance? (Round your answer to 6 decimal places.)

Probability

The United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different locations.

(a) What is the probability that all six arrive within two days? (Round your answer to 4 decimal places.)

Probability

(b) What is the probability that exactly five arrive within two days? (Round your answer to 4 decimal places.)

Probability

(c) Find the mean number of letters that will arrive within two days. (Round your answer to 1 decimal place.)

Number of letters

(d-1) Compute the variance of the number that will arrive within two days. (Round your answer to 3 decimal places.)

Variance

(d-2) Compute the standard deviation of the number that will arrive within two days. (Round your answer to 4 decimal places.)

Standard Deviation

A CD contains 10 songs; 6 are classical and 4 are rock and roll.

In a sample of 3 songs, what is the probability that exactly 2 are classical? Assume the samples are drawn without replacement. (Round your answer to 2 decimal places.)

Probability

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 6.4 emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.

(a) What is the probability Linda Lahey, company president, received exactly 3 email between 4 P.M. and 5 P.M. yesterday? (Round your answer to 4 decimal places.)

Probability

(b) What is the probability she received 8 or more emails during the same period? (Round your answer to 4 decimal places.)

Probability

(c) What is the probability she received four or less email during the period? (Round your answer to 4 decimal places.)

Probability

Suppose the Internal Revenue Service is studying the category of charitable contributions. A sample of 34 returns is selected from young couples between the ages of 20 and 35 who had an adjusted gross income of more than $100,000. Of these 34 returns 8 had charitable contributions of more than $1,000. Suppose 7 of these returns are selected for a comprehensive audit.

(a) You should use the hypergeometric distribution because

(b) What is the probability exactly one of the seven audited had a charitable deduction of more than $1,000? (Round your answer to 4 decimal places.)

Probability

(c) What is the probability at least one of the audited returns had a charitable contribution of more than $1,000? (Round your answer to 3 decimal places.)

Probability

Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random sample of 200 antennas, find the probability that: (Use the poisson approximation to the binomial.)

(a) None of the antennas are defective. (Round your answer to 4 decimal places.)

Probability

(b) Three or more of the antennas are defective. (Round your answer to 4 decimal places.)

Probability

The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 6 of the 35 possible numbers. Assume there are 35 ping-pong balls each with a single number between 1 and 35. Any number appears only once, and the winning balls are selected without replacement.

(a) The commission reports that the probability of matching all the numbers are 1 in 1,623,160. What is this in terms of probability? (Round your answer to 8 decimal places.)

Probability

(b) Find the probability, again using the hypergeometric formula, for matching 4 of the 6 winning numbers. (Round your answer to 8 decimal places.)

Probability

(c) Find the probability of matching 5 of the 6 winning numbers. (Round your answer to 8 decimal places.)

Probability

In a binomial distribution and . Find the probabilities of the following events. (Round your answers to 4 decimal places.)

(a)

Probability

(b)

Probability

(c)

Probability

A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames:

(a) None will need adjustment? (Round your answer to 3 decimal places.)

Probability

(b) At least one will need adjustment? (Round your answer to 3 decimal places.)

Probability

(c) More than two will need adjustment? (Round your answer to 3 decimal places.)

Probability

Three tables listed below show random variables and their probabilities. However, only one of these is actually a probability distribution.

(a) Which is it?

A B C

x P(x) x P(x) x P(x)

5 .2 5 .2 5 .3

10 .3 10 .2 10 .2

15 .1 15 .1 15 .2

20 .7 20 -.5 20 .3

(b) Using the correct probability distribution, find the probability that x is: (Round your answers to 1 decimal place.)

(a) P(Exactly 15) =

(b) P(No more than 10) =

(c) P(More than 5) =

c) Compute the mean, variance, and standard deviation of this distribution. (Round your answers to 2 decimal places.)

(a) Mean µ

(b) Variance σ2

(c) Standard deviation σ

The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience.

Admissions Probability

1,030 0.2

1,380 0.2

1,580 0.6

________________________________________

(1) What is the expected number of admissions for the fall semester? (Round your answers to the nearest whole number.)

Expected number of admissions

(2) Compute the variance and the standard deviation of the number of admissions. (Round your answers to 2 decimal places.)

Variance

Standard deviation

In a recent study 90 percent of the homes in the United States were found to have largescreen TVs. In a sample of nine homes, calculate the probabilities.

(a) All nine have large-screen TVs. (Round your answer to 3 decimal places.)

Probability

(b) Less than five have large-screen TVs. (Round your answer to 3 decimal places.)

Probability

(c) More than five have large-screen TVs. (Round your answer to 3 decimal places.)

Probability

(d) At least seven homes have large-screen TVs. (Round your answer to 3 decimal places.)

Probability

Compute the mean and variance of the following discrete probability distribution.

X P(x)

2 .5

8 .3

10 .2

________________________________________

(Round your answers to 2 decimal places.)

(1)

μ =

(2)

σ ² =

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 234 customers on the number of hours cars are parked and the amount they are charged.

Number of Hours Frequency Amount Charged

1 17 $3

2 35 8

3 49 10

4 44 16

5 33 22

6 15 24

7 9 28

8 32 30

234

________________________________________

(a) Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

Hours Probability

1

2

3

4

5

6

7

8

________________________________________

(b-1) Find the mean and the standard deviation of the number of hours parked. (Round your intermediate values and final answers to 3 decimal places.)

Mean

Standard deviation

(b-2) How long is a typical customer parked? (Round your answer to 2 decimal places.)

The typical customer is parked for hours

(c) Find the mean and the standard deviation of the amount charged. (Round your intermediate values and final answers to 3 decimal places.)

Mean

Standard deviation

Check My WorkeBook Link References

Worksheet Difficulty: Medium Learning Objective: 06-3

Which of these variables are discrete and which are continuous random variables?

(a) The number of new accounts established by a salesperson in a year.

(b) The time between customer arrivals to a bank ATM.

(c) The number of customers in Big Nicks barber shop.

(d) The amount of fuel in your cars gas tank.

(e) The number of minorities on a jury.

(f) The outside temperature today.

It is reported that 32 percent of American households use a cell phone exclusively for their telephone service. In a sample of fourteen households, find the probability that:

(a) None use a cell phone as their exclusive service. (Round your answer to 4 decimal places.)

Probability

(b) At least one uses the cell exclusively. (Round your answer to 4 decimal places.)

Probability

(c) At least eight use the cell phone. (Round your answer to 4 decimal places.)

Probability

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 250 customers on the number of hours cars are parked and the amount they are charged.

Number of Hours Frequency Amount Charged

1 20 $3.00

2 38 6.00

3 53 9.00

4 45 12.00

5 40 14.00

6 13 16.00

7 5 18.00

8 36 20.00

250

________________________________________

(a-1) Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.)

Hours Probability

1

2

3

4

5

6

7

8

(a-2) Is this a discrete or a continuous probability distribution?

(b-1) Find the mean and the standard deviation of the number of hours parked. (Round your answer to 2 decimal places.)

Mean

Standard deviation

(b-2) How long is a typical customer parked? (Round your answer to 2 decimal places.)

The typical customer is parked for

(c) Find the mean and the standard deviation of the amount charged. (Round your answer to 2 decimal places.)

Mean

Standard deviation

It is asserted that 60 percent of the cars approaching an individual toll booth in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of five cars:

(a) All five will have the transponder. (Round your answer to 4 decimal places.)

Probability

(b) At least two will have the transponder. (Round your answer to 4 decimal places.)

Probability

(c) None will have a transponder. (Round your answer to 6 decimal places.)

Probability

Listed below is the population by state for the 15 states with the largest population. Also included is whether that state’s border touches the Gulf of Mexico, the Atlantic Ocean, or the Pacific Ocean (coastline).

Rank State Population Coastline

1 California 35,893,799 Yes

2 Texas 22,490,022 Yes

3 New York 19,227,088 Yes

4 Florida 17,397,161 Yes

5 Illinois 12,713,634 No

6 Pennsylvania 12,406,292 No

7 Ohio 11,459,011 No

8 Michigan 10,112,620 No

9 Georgia 8,829,383 Yes

10 North Carolina 8,541,221 Yes

11 New Jersey 8,698,879 Yes

12 Virginia 7,459,827 Yes

13 Washington 6,203,788 Yes

14 Massachusetts 6,416,505 Yes

15 Indiana 6,237,569 No

________________________________________

Suppose four states are selected at random. Calculate the probability for the following:

(a) None of the states selected have a population of more than 12000000 (Round your answer to 3 decimal places.)

Probability

(b) Exactly one of the selected states has a population of more than 12000000 (Round your answer to 2 decimal places.)

Probability

(c) At least one of the selected states has a population of more than 12000000 (Round your answer to 3 decimal places.)

Probability

See attached file.

Need Help

For #70a, b I know I have to use the complement like

1- (p(all four people with no good blood)) but do I multiply each probability or add them?

For #66 not sure how begin this one

For #63 I feel as if i don’t have enough info to start with.

For # 29,29b I get values that are way off the correct answers,

like a) 138783/469491 b) .2965/(107632/156499) …

i’m probably adding the wrong values. theres just a lot to choose from.

For #39 I would think the answer would just be 70% because its given but no its wrong.

filename answer

=========================

39 .8235

29 a).4979 b).5144 c).7443 d).4399 e).6894

63 a).216 b).936 c).648

66 .5952

70 .8704

Can you please say which formula you’re using if any. It’s hard for me to understand problems with percents. We have just covered Bayes rule, conditional probability, multiplicative rule, additive rule, complement and independence.

Is there any book that you recommend for help as well, it would be helpful as well.

Thanks,

1. Suppose you have 3 nickels, 2 dimes, and 6 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that

a. You will draw a dime?

b. You will draw a nickel?

c. You will draw a quarter?

2. You are rolling a pair of dice, one red and one green. What is the probability of the following outcomes:

a. The sum of the two numbers you roll from the dice is 8.

b. The sum of the two numbers you roll is 12.

c. The sum of the two numbers you roll is 7.

3. For this question pretend you are drawing cards without replacement from the infamous “Iraq’s Most Wanted” deck issued by the U.S. Military before Saddam Hussein and his gang were killed or captured. If you are drawing from the full deck of 52 cards (no jokers), what are the following probabilities:

a. You draw a card that is not Saddam Hussein

b. You draw two cards, which end up being Saddam Hussein and another one with his cousin “Chemical Ali”.

c. You draw 14 cards and not one of them is Saddam Hussein [Note: this is a tough one. Please show your work so that even if you didn’t get the right answer you can still get partial credit.

Please complete answer/steps/explanation for the following:

2.7.11. An apartment building has eight floors. If seven people get on the elevator on the first floor, what is the probability they all want to get off on different floors? On the same floor? What assumption are you making? Does it seem reasonable? Explain.

Having problem with probability of statistical problem. Need assistance with step by step showing formula.

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average US driver takes 50,000 trips. (A) What is the probability of a fatal accident over a lifetime? Assume independent events. Why might the assumption of independence be violated?

The sign “I LOVE MATHEMATICS” is put on the wall of the mathematics building at South Central Carolina Technical College. The letters start to fall off of the sign. Find the probability of each of the following events.

1.. The first letter that falls off is “M” .

2. The second letter that falls off is an “A” knowing that the first letter that fell off was a “M”

In testing a new drug, researchers found that 5% of all patients using it will have a mild side effect. A random sample of 11 patients using the drug is selected. Find the probability that:

a) exactly two will have this mild side effect

b) at least one will have this mild side effect.

1. There are 3 boxes. Each box contains several envelopes. Some envelopes have “you lose” written on them. The rest say “you win…” . However, of the ones that say “you win…” , some contain only a piece of paper saying “… nothing” . Each of the other contains a $5 bill.

The first box contains 3 “lose” envelopes and 2 so-called “win” envelopes. The second contains 1 “lose” envelope and 3 “win “envelopes. The third box contains 2 “lose” envelopes and 2 “win” envelopes. Each box contains only one $5 bill(in an envelope marked” you win…”).

Addie, who is blindfolded, selects a box at random and draws one envelope from the box. The envelope contains a $5 bill. What is the probability that Addie picked the second box?

Problem 4.

Let X denote the number of boys in a family with four children.

Pr(X > 3) is?

a. 5/16

b. ¼

c. 11/16

d. 2/3

e. None of the above

Suppose the probability that a federal income tax return conatins an arithemetic error is 0.2. If 10 federal income tax returns are selected at random, the probability that fewer than two of them will conatin errors is:

Population mean = 18.4%, standard deviation = 20%, sample size= 25. Find the probability that the sample mean is less than 20%.

A standardized test consists entirely of multiple-choice questions, each with 5 possible choices. You want to ensure that a student who randomly guesses on each question will obtain an expected score of zero. How would you accomplish this?

Some parts of California are particularly earthquake-prone. Suppose that in one such area…

a) Find the probability distribution of X…

Please see attached.

Problem

Assume that E[|X-2|³]=5. Give a lower estimate for P[-2<X<6]

Please see attached.

Fluctuation in the prices of precious metals such as gold have been empirically shown to be well approximated by a normal distribution when observed over short interval of time. In May 1995, the daily price of gold (1 troy ounce) was believed to have a mean of $383 and a standard deviation of $12. A broker, working under these assumptions, wanted to find the probability that the price of gold the next day would be between $394 and $399 per troy ounce. In this eventuality, the broker had an order from a client to sell the gold in the client’s portfolio. What is the probability that the client’s gold will be sold the next day?

For the following questions, would the following be considered “significant” if its probability is less than or equal to 0.05?

a) Is it “significant” to get a 12 when a pair of dice is rolled?

b) Assume that a study of 500 randomly selected school bus routes showed that 480 arrived on time. Is it “significant” for a school bus to arrive late?

Suppose that the demand for a company’s product in weeks 1, 2, and 3 are each normally distributed and the mean demand during each of these three weeks is 50, 45, and 65, respectively. Suppose the standard deviation of the demand during each of these three weeks is known to be 10, 5, and 15, respectively. It turns out that if we can assume that these three demands are probabilistically independent then the total demand for the three week period is also normally distributed. And, the mean demand for the entire three week period is the sum of the individual means. Likewise, the variance of the demand for the entire three week period is the sum of the individual weekly variances. But be careful! The standard deviation of the demand for the entire 3 week period is not the sum of the individual standard deviations. Square roots don’t work that way!

Now, suppose that the company currently has 180 units in stock, and it will not be receiving any further shipments from its supplier for at least 3 weeks. What is the probability that the company will run out of units?

Please help with the following problems.

Among females in the United States between 18 and 74 years of age, diastolic blood pressure (DBP) is normally distributed with mean ? = 76 mm Hg and standard deviation ? = 10.2 mm Hg.

a) What is the probability that a randomly selected woman has a DBP less than 65 mm Hg?

b) What is the probability that she has a DBP greater than 95 mm Hg?

c) What is the probability that the woman has a DBP between 65 and 95 mm Hg?

d) Assume you want to concentrate on the individuals with low DBP, but you do not have the explicit definition of the cutoff value for low DBP. You decide to look at the people with lowest DBP that constitute 3.51% of the population. What cutoff value of DBP would split off or demarcate the lowest-DBP 3.51% of the population?

Suppose that infants are classified as low birth weight if they have birth weight 2500g, and as normal birth weight if have birth weight 2501g. Suppose that infants are also classified by length of gestation in the following four categories: <20 weeks, 20-27 weeks, 28-36 weeks, >36 weeks. Assume the probabilities of the different period of gestation are as given in the table below:

See attached for table.

Also assume that the probability of low birth weight given that length of gestation is <20 weeks is .540, the probability of low birth weight given that length of gestation is 20-27 weeks is .813, the probability of low birth weight given that length of gestation is 28-36 weeks is .378, and the probability of low birth weight given that length of gestation is >36 weeks is .031.

a) What is the probability of having a low birth weight infant?

b) Show that the events {length of gestation 27 weeks} and {low birth weight} are not independent.

The Northside Rifle team has two marksperson, Dick and Sally. Dick hits a bull’s-eye 90% of the time, and Sally hits a bull’s-eye 95% of the time.

(a) What is the probability that either Dick or Sally or both will hit the bull’s-eye if each takes one shot?

(b) What is the probability that Dick and Sally with both hit the bull’s-eye?

There is a 0.1081 probability that a best-of-seven contest will last four games, a 0.1171 probability that it will last five games, a 0.2466 probability that it will last six games, and a 0.5282 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation. Is it unusual for a team to “sweep” by winning in four games?

a. What is the mean of the probability distribution (Round to two decimal places as needed) ________.

b. What is the standard deviation of the probability distribution (Round to two decimal places as needed) _______

Is it unusual for a team to win in four games? Choose the correct response below.

(1) Yes, because the probability that a team wins in four games is less than or equal to 0.05

(2) No, because the probability that a team wins in four games is greater than 0.05

(3) No, because the probability that a team wins in four games in less than or equal to 0.05

(4) Yes, because the probability that a team wins in four games is greater than 0.05

Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative growth (Business Week, July 30, 2001). For a sample of 20 Americans, make the following calculations:

a. Compute the probability that exactly 12 people believed the country was in a recession.

b. Compute the probability that no more than five people believed the country was in a recession.

c. Howmany people would you expect to say the county was in a recession?

d. Compute the variance and standard deviation of the number of people who believed the country was in a recession.

Each item produced by a certain manufacturer is, independantly, of acceptable quality with probability 0.95. Approximate the probability that at most 10 of the next 150 items produced are unacceptable.

30) An image is partitioned into 2 regions – one white and the other black. A reading taken from a randomly chosen point in the white section will give a reading that is normally distributed with Mean=4 and Variance =4, whereas one taken from a randomly chosen point in the black region will have a normally distributed reading with parameters (6,9). A point is randomly chosen on the image and has a reading of 5. If the fraction of the image that is black is alpha, for what vlaue of alpha would the probability of making an error be the same whether one concluded the point was in the black region or in the white region?

NOTE: Black is N(6, 3) (9 = variance)

A music store has jazz, classical, country western, and rock music albums on tapes and CDs in the following quantities:

Jazz Classical Country

Western Rock Total

Tape 46 14 36 53 149

CD 38 53 22 19 132

Total 84 67 58 72 281

a. Form a related table with entries that are relative frequencies (three decimal places).

Based on the relative frequencies, estimate the probability that an album selected at random is a

b. rock album

c. classical CD or country western CD

d. jazz or classical album

e. CD

(Please see attachment for table)

In the game of Two-Finger Morra, 2 players show 1 or 2 fingers and simultaneously guess the number of fingers their opponent will show. If only one of the players guesses correctly he wins the amount (in dollars) equal to the sum of the fingers shown by him and by his opponent. If both players guess correctly or neither guesses correctly, then no money is exchanged. Consider a specified player and denote by X the amount of money he wins in a single game of Two-Finger Morra …

*(Please see attachment for complete question)

Suppose that it takes at least 9 votes from a 12-member jury to convict a defendant. Suppose the probability that a juror votes a guilty person innocent is 0.2. whereas the probability that the juror votes an innocent person guilty is 0.1. If each juror acts independently and if 65% of the defendants are guilty, find the probability that the jury renders a correct decision. What % of defendants are convicted?

Dear OTA,

Please help me with steps.

Thanks

A family has 4 children. The probability of having a boy is 50% (girl is the same 50%).

1) What is the probability that the family only has one boy?

2) What is the probability that the family only has three boys?

3) What is the probability that the family has at least one boy?

4) What is the probability that 4 children are girls?

Suppose that the probability that a person will develop hypertension over a lifetime is 20%.

5) What is the probability that 4 or 5 people develop hypertension over a lifetime among 20 students graduating from the same high school class?

6) What is the probability that exactly 3 people develop hypertension over a lifetime among 20 students graduating from the same high school class?

7) What is the probability that at least 2 people develop hypertension over a lifetime among 20 students graduating from the same high school class?

Two people are selected at random.

What is the probability both born on Monday?

Please provide a formula and answer.

Please help with the following problem:

Assume that the dollar loss, L, associated with being robbed by a mugger on the street is $3, and that being robbed occurs with a probability of p. Suppose an individual can influence p by exercising caution, but doing so will be costly. Let the cost, C, required to achieve probability p be given by C=4(1-p)^3. Assume that the individual is risk neutral.

a. If insurance is not available, what probability of loss will the agent choose?

Now, assume an insurance policy that pays the full amount of the loss (if it occurs) is now available at a total premium or price Z (i.e., the policy cost is Z, not ZL). Then,

b. If insurance has already been purchased, what probability of a loss will

the agent choose? Given your answer to this, what premium must an

insurance company charge in order to “break even?”

c. Using the answers obtained from part a and b, prove that a risk neutral

agent will not purchase any insurance at the premium that must be

charged in order for the insurance company to break even.

Please see attachment for question.

Please do these two things when solving the problem:

i) Use words to describe the solution process

ii) If you use a theorem or proposition, please state what it is called and your source. For example, THEOREM 3.1, ROSS, CHP 3.

The probability of a coat having a defect is 1/3. What is the probability of there being 15 defective coats in a batch?

Half of a set of the parts are manufactured by machine A and half by machine B. Four percent of all the parts are defective. Six percent of the parts manufactured on machine A are defective. Find the probability that a part was maufactured on machine A, given that the part is defective. Explain your reasoning clearly.

Please show how you get all calculations for the answer

1. There is a 20% probability of rain tomorrow means that:

a. Tomorrow it will be raining during 0.2 of the day, and the rest of the day it will be clear.

b. Out of the next 5 days, one day it will be raining.

c. According to the records, if a weather like one we have today occurred in the past, then 20% of cases it was raining on the next day.

What is wrong?

2. You brought 10 lottery tickets. One of them won prize. That means probability of winning a prize is 1/10.

True or False?

3. In a lottery, the more tickets you buy, the more chance you have to win the prize(s).

True or False?

4. If you have 3 suits, 10 shirts, and 12 neckties, you can come to work each time in a different outfit during the whole year.

True or False?

The probability that a family with 6 children has exactly four boys is:

a. 1/3

b. 1/64

c. 15/64

d. 3/8

e. none of the above

10. Ninety-eight percent of all babies survive delivery. However, 15 percent of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 96 percent of the time. If a randomly chosen pregnant woman does not have a C section, what is the probability that her baby survives?

6. If there are 12 strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?

Two separate questions below:

A.) A bin contains 20 fuses of which 5 will be defective. If 2 fuses are selected at random without replacement, what is the probability that at most, one is defective?(Please show equation)

B.) From a group of 5 men and 6 women, how many committees of size 3 are possible with 2 men and one women if a certain man must be on the committee?

(Please show equation)

Suppose someone offers to pay you $100 if you draw 3 cards from a standard deck of 52 cards and all the cards are clubs. What should you pay for the chance to win if it is a fair game?

I encourage you to use PHStat as much as possible and attach PHStat outputs to your work. No manual calculation is required.

[1] As reported by Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Let x be the finishing time for a finisher in the New York 10-km run.

a) What is the chance that finishers complete the run with the times between 50 and 70 minutes?

b) What is the chance that finishers complete the run with the times more than 75 minutes?

c) How fast would finishers have to complete the run among the top 5% finishers?

[2] In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg Atorvastatin tablets. Among them, 19 patients experienced flu symptoms and 844 patients did not (based on data from Pfizer, Inc.).

a) Estimate the probability that one patient taking the drug will experience flu symptoms.

b) Is this unusual for a patient taking the drug to experience flu symptoms? Explain.

c) If you know that the probability of flu symptoms for a person not receiving any treatment is 0.019, what is the probability that there are 19 who experience flu symptoms among 863 patients? Explain.

d) Is this unusual to find that among 863 patients, there are 19 who experience flu symptoms in c)? Explain.

[3] On average, 70 percent of the passengers on a flight from San Francisco to Boston prefer chicken to fish. Assume that the passengers have only one of two choices, chicken or fish for their meal. If there are 200 passengers on a flight and the airline carries 140 chickens and 60 fish dinners, what is the probability that more than five passengers will be disappointed?

[4] A recent Gallup poll consisted of 1012 randomly selected adults who were asked whether “cloning of humans should or should not be allowed.” Results showed that 89% of those surveyed indicated that cloning should not be allowed.

a) If we assume that people are indifferent so that 50% believe that cloning of humans should not be allowed, find the mean and standard deviation for the numbers of people in groups of 1012 that can be expected to believe that such cloning should not be allowed.

b) Based on the preceding results, does the 89% result for the Gallup poll appear to be unusually higher than the assumed rate of 50%? Does it appear that an overwhelming majority of adults believe that cloning of humans should not be allowed?

If P is a normally distributed random variable with a mean of 50 and a standard deviation of 2, what is the probability that P is between 47 and 54?

3. Historically, demand for a product has been normally distributed. You collect 12 months of

demand data (shown in Demand tab). Use this data to estimate your population parameters.

a. What is the probability that demand will be equal to the mean?

b. What is the probability that demand will be less than the mean?

c. Demand under 450 is considered “low”. What is the probability of low demand?

d. Demand between 450 and 600 is “typical”. What is the probability of typical demand?

e. Demand between 600 and 700 is “high”. What is the probability of high demand?

f. You do an inventory check and find that you have only 700 units of product on hand. If demand is greater than 700, you will have a shortage, which is bad for business. What is the probability that demand will be greater than 700?

g. In order to avoid shortages, how much inventory should you keep on hand so that shortages only happen during the top 1% of highest demand? In other words, how can you be 99% certain that all demand will be met?

A bicycle plant runs two assembly lines, A and B. 96.3% of line A’s products pass instruction, while only 92.1% of line B’s products pass inspection, and 70% of the factory’s bikes come off assembly line A.

a) What is the probability that a randomly selected bike passed inspection?

b) What is the probability that a randomly selected bike that did not pass inspection came from assembly line B?

A box contains 4 green, 10 red, 6 yellow, and 5 blue marbles. Four marbles are drawn from the box without replacement.

a) What is the probability that you get one marble of each color??

b) What is the probability that none of the marbles is red?

c) What is the probability that all four marbles are the same color

Please specify the terms you use (if necessary) and explain each step of your solutions. Thank you very much.

2. Twenty workers are to be assigned to 20 different jobs, one to each job. How many different assignments are possible?

3. A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many if she must answer at least 3 of the first 5 questions?

4. A dance class consists of 22 students, 10 women and 12 men. If 5 men and 5 women are to be chosen and then paired off, how many results are possible?

1. If the probability of an event is .857, what is the probability that the event will not occur?

2. A baseball player with a batting average of .300 comes to bat. What are the odds in favor of the ball player getting a hit?

34. Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked as an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it? Repeat under the assumption that the lifetime mileage of the car is not exponentially distributed but rather is (in thousands of miles) uniformly distributed over (0, 40).

3. Presume in community 1, 52% of individuals who will vote in election favor candidate A while while 48% favor candidate B. In community 2, 46% favor candidate A and 54% favor B. Community 1 is four times as large as community 2. Prior to election, a poll of 1000 randomly selected voters is taken with 800 from community 1 and 200 coming from community 2. The poll will correctly predict that A will win if the majority of poll says they favor A

3a) What is prob. that first person polled favors A?

3b) If first person polled favors B, what is prob. that the individual comes from community 1?

3c) What is the prob. the poll predicts that B will win.

3d) Presume a second independent poll of 1000 voters (800 from community 1 and 200 from 2). What is prob. A is predicted the winner by one poll and B is predicted the winner by the other?

3e) If the 1000 voters in each poll are put together to form a poll of 2000 voters, what is prob. A is predicted to win?

￼

1. The number of hours needed by students in a science class to complete a research project was recorded with the following results:

hours Number of Students(freq)

0 – 14 2

15 – 29 4

30 – 44 10

45 – 59 16

60 – 74 6

75 – 89 2

A student is selected at random. Find the following probabilities.

a. The student took between 5 and 9 hours, inclusive.:

b. The student took at least 6 hours.

c. The student took less than 5 hours.

A jar contains marbles of different colors: 4 white, 6 black, 6 red, and 4 blue. On two random drawings, without replacement, find the probability that the first is black and the second is white. Assume that the draws are independent.

The animal colony in the reseach department contains 20 male rats and 30 female rats. Of the 20 males, 15 are white and 5 spotted. Of the 30 females, 15 are white, and 15 are spotted. Suppose that you randomly select 1 rate from this colony:

a)Find the Joint probability table including the marginal probability.

b) what is the probability of obtaining 1 female

c)what is the probability of obtaining a white male

d) which selection is more likely; a spotted male or a spotted female.

e)Given that a rat is female, what is the probability that it is spotted.

Take a deck of cards. A deeck has 52 cards with two major colors(Red and Black), with 26 cards each. Red colors comes in two shapes(heart and diamond), while black color shapes are called clubs and spades.

Find the probability of obtaining Red or Queen. That is, find Probability(Red or Queen).

A particular test for the presence of steroids is to be used after a professional track meet. If steroids are present, the test will accurately indicate this 95% of the time. However, if steroids are not present, the test will indicate this 90% of the time (so it is wrong 10% of the time and predicts the presence of steroids). Based on past data, it is believed that 2% of the athletes do use steroids. This test is administered to one athlete, and the test is positive for steroids. What is the probability that this person actually used steroids?

A group of n people meet at lunch for a cup of coffee. They play a game to see who gets to pay for all the coffees. Each person flips a coin. If all the coins come up the same except for one person, then that one person gets to pay for all the coffee. If the coins do not result in this way, then everyone flips again until there is exactly one person different. Obviously, the game doesn’t work for less than three people. Also, as n grows large it may take many flips to decide the loser of the game.

(a) For n = 3 people, how many flips will it take on average to find a winner?

(b) For n = 10 people, how many flips will it take on average to find a winner?

(c) Find a general formula that computes the average number of flips as a function of n. Create a graph for n = 3…20 showing the number of required flips.

How many ways can 6 distinguishable balls be placed in 5 boxes such that there are 2 balls in the first box, and one in all remaining boxes?

A company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly saying a good item is defective. The company has evidence that its production is 0.9% defective.

a.) What is the probability that an item selected for inspection is classified as defective?

b.) If an item randomly selected is classified as nondefective. What is the probability that it is really good?

Value Proportion

0 0.17

2 0.35

3 0.33

4 0.15

a.) Determine the cumulative distribution function of the Value.

b.) Determine the mean and variance of the Value.

Fran and Ron play a series of independent games. Fran’s probability of winning any particular game is 0.6 (and Ron’s probability of winning is therefore 0.4). Suppose that they play a best-of-5 tournament. (That is, the winner of the tournament is the first person to win 3 games.)

1. Find the probability that Fran wins the tournament in 3 games.

1) _______________

2. Find the probability that the tournament lasts exactly 3 games.

2) _______________

3. Find the probability that the tournament lasts exactly 4 games.

3) _______________

4. Find the probability that Fran wins the tournament.

4) _______________

5. Find the probability that the tournament lasts exactly 3 games if it is won by Fran.

5) _______________

6. Find the probability that Fran won the tournament if it lasted exactly 3 games.

6) _______________

Subject: Probability

Details: You appear on a game show and for your prize the host lets you choose one of three doors. Behind one door is a new car; behind each of the other doors is a goat. You choose a door. The host, who knows what’s behind each door, then opens another door, which has a goat. He then asks if you want to pick the remaining door. If you switch you choice of doors, what is the porbability of getting the door with the new car?

Al, Bob and Carlos are playing a silly game. Al flips a coin. If he gets heads, the game ends and he wins. If not, Bob flips the coin. If he gets heads, the game ends and he wins. If not, Carlos flips the coin. If he gets heads, the game ends and he wins. If not, the coin is returned to Al and the entire process begins again. The game continues until soneone gets heads. What is the probability of each of them winning?

Please explain this in a way that is comprehensible to a 9th grader.

The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is

given by f(x) = (ax2e−bx2 x>_0 { 0 x < 0

where b = m/2kT and k, T and m denote, respectively, Boltzmann’s constant, the absolute temperature, and the mass of the molecule. Evaluate a in terms of b.

(Additionaly, its ax(to the 2nd)e (to the -bx(to the 2nd) and then x is greater than or equal to 0)

Question: Urn I has 2 white and 3 black balls; Urn II, 4 white and 1 black; and Urn III, 3 white and 4 black. An urn is selected at random and a ball drawn at random is found to be white. Find the probability that Urn I was selected.

Answer: 14/57

The chart below gives the number or vehicle tags sold in each city.

CITY NUMBER OF VEHICLE TAGS SOLD

bristol 1,863

trevor 3,507

camp lake 2,457

salem 1,773

paddock lake 2,541

One car is selected at random from the cars with vehicle tags from these cities, What is the probability that this car is from Salem?

1. A city had an average of 2.6 lightning storms per month. What is the probability of at least 3 lightning storms during a month?

A. 12.26%

B. 21.76 %

C. 26.40%

D. 48.16%

E. none of the above

2. If the number of miles per gallon (mpg) achieved by cars of a particular model has a mean of 25 and a standard deviation of 2, what is the probability that, for a random sample of 20 such cars, the average mpg will be less than 24? Assume population distribution is normal.

A. 0.125

B. .1443

C. .2875

D .3026

E. none of the above

A manufacturer of window frames know from long experience that 5 percent of the production will have some type of minor defect tht will require an adjustment. What is the probability that in a sample of 20 window frames

a) none will need adjustment

b) at least one will need adjustment

c) More than two will need adjustment

The events A and B are mutually exclusive. Suppose P(A)=0.30 and P(B)=0.40. What is the probability of either A or B occurring? what is the compliment of event A? What is the meaning?

The funds dispensed at the atm machine located near the checkout line at the krogers in union, kentucky, follow a normal probability distribution with a mean of $4,200 a day and a standard deviation of $720 a day. The machine is programmed to notify the local bank if the amount dispensed is very low ( less an $2,500) or very high (more than $6,000).

a. What percent of the days will the bank be notified because the amount dispensed is very low.

b. What percent of the time will the bank be notified because the amount dispensed is to high.

c. What percent of the time will the bank not be notified reguarding the amount of funds dispersed.

Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount of tip a server can expect to earn per check (or bill). A study of 500 recent checks indicated the server earned the following tip.

Amount of Tip Number

$ 0 up to $ 5 200

5 up to 10 100

10 up to 20 75

20 up to 50 75

50 or more 50

Total 500

1. What is the probability of a tip of $50 or more?

2. Are the categories “$0 up to $5,” “$5 up to $10,” and so on considered mutually exclusive? If the probabilities associated with each outcome were totaled, what would that total be?

3. What is the probability of a tip of up to $10?

4. What is the probability of a tip of less than $50?

According to the National Climatic Data Center, Miami, Florida experienced 138 days of measurable precipitation (rain) in 1995. By comparison, the weather station at Phoenix, Arizona reported 31 days of precipitation during the same year. Neither amount of precipitation was considered unusual for these two cities.

a. A day is selected randomly for a pleasure trip to Miami. What is the probability that it will rain while you are there?

b. A day is selected randomly for a pleasure trip to Phoenix. What is the probability that it will rain while you are there?

An industrial oven used to cure san cores for a factory manufacturing engine blocks for small cars is able to maintain fairly constant temperatures. The temperature range of the oven follows a normal distribution with a mean of 450 F and a standard deviation of 25 F. Leslie Larsen, president of the factory is concerned about the large number of defective cores that have been produced in the past several months. If the oven gets hotter than 475 F, the core is defective. What is the probability that the oven will cause a core to be defective? What is the probability that the temperature of the oven will range from 460 to 470 F?

In the questions I have below it says a bowl has eight ping pong balls numbered 1,2,2,3,4,5,5,5. You pick a ball at random.

a. Find p(the number on the ball drawn is ≥ 3).

b. Find p(the number on the ball drawn is even).

A.)AN UNBIASED COIN IS FLIPPED 5 TIMES. WHAT IS THE PROBABILITY OF GETTING EXACTLY 1 HEAD ON THE 5 TRIALS?

B.)WHAT IS THE PROBABILITY OF GETTING AT LEAST ONE HEAD IN THE 5 TRIALS?

Question 1 (5 points)

Chose a simple random sample of size five (5) from the following employees of a small company.

1. Bechhofer 4. Kesten 7. Taylor

2. Brown 5. Kiefer 8. Wald

3. Ito 6. Spitzer 9. Weiss

Use the numerical labels attached to the names above and the following list of random digits. Read the list of random digits from left to right, starting at the beginning of the list.

11003 20131 05907 11384 44982 20751 27498 12009 45287

The simple random sample is

a. Bechhofer, Brown, Ito, Kiefer, and Weiss.

b. Bechhofer, Ito, Kiefer, Taylor, and Weiss.

c. Bechhofer, Brown, Ito, Kesten, and Wald.

d. Brown, Ito, Kesten, Spitzer, and Wald.

Save answer

Question 2 (5 points)

A survey conducted by Black Flag asked whether the action of a certain type of roach disk would be effective in killing roaches. 79 percent of the respondents agreed that the roach disk would be effective. The outcome, 79 percent, is a

a. sample space.

b. simple outcome.

c. statistic.

d. synonym.

Save answer

Question 3 (5 points)

The experiment is to roll a six-sided die and to observe which side comes up. The collection of specific outcomes that could occur as a result of the experiment is known as the

a. an event.

b. simple outcome.

c. statistic.

d. synonym.

Save answer

Question 4 (6 points)

You have a vase that contains 5 red, 4 white, and 3 blue marbles. You reach into the vase a draw a marble. What is the probability that the marble selected is white [P(W)]?

a. 0.5833

b. 0.4167

c. 0.3333

d. 0.25

Save answer

Question 5 (6 points)

The experiment is to pick a card from a deck of ten (10) cards, numbered 1 through 10, and flip a two-sided coin labeled “heads” on one side “tails” on the other.

Event A represents observing an even numbered card.

Event B represends observing a “head” on the coin.

What is the probability that event A and B occur as a result of the experiment?

a. 0.2500

b. 0.5000

c. 0.7500

d. 1.0000

Save answer

Question 6 (6 points)

You have a vase that contains 5 red, 4 white, and 3 blue marbles. You reach into the vase a draw a marble. What is the probability that the marble selected is red and white [P(R and W)]?

a. 0.0000

b. 0.2500

c. 0.3333

d. 0.4167

Save answer

Question 7 (5 points)

You have a deck of cards numbered 1 through 10. You select a card. What is the probability that the card selected has an odd number or a number less than 6 [P(O or <6)]?

a. 0.2500

b. 0.5000

c. 0.7000

d. 1.0000

Save answer

Question 8 (6 points)

You have a deck of cards numbered 1 through 10. You select a card. What is the probability that the card selected has an odd number and a number less than 6 [P(O and <6)]?

a. 0.0000

b. 0.2500

c. 0.3000

d. 0.7000

Save answer

Question 9 (6 points)

As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that at least 80 percent have committed rule violations [P( ≥ 80%)]?

a. 0.0838

b. 0.5838

c. 0.8000

d. 0.9162

Save answer

Question 10 (6 points)

The ABC Company has manufactured light bulbs for the last 75 years. During this time the company has established a defective rate of 10%. As part of the quality control process random samples of 50 light bulbs are selected for testing.

What is the probability that at least 5% of the light bulbs are defective [P( ≥ 5%)]?

a. 0.1193

b. 0.3333

c. 0.8807

d. 1.0000

Save answer

Question 11 (6 points)

As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that the proportion of program committing rule violations this year will exceed the norm by at least 5 percent [P( – p ≥ 5%)]?

a. 0.2451

b. 0.4902

c. 0.7451

d. none of the above

Save answer

Question 12 (10 points)

As NCAA investigators continue to probe deeper into college sports, an offical indicates that 70 percent of collegiate basketball programs violate NCAA rules. Out of 40 programs examined this year, what is the probaility that no more than 25 percent have committed rule violations [P( ≤ 25%)]?

a. 1.0000

b. 0.7500

c. 0.3333

d. 0.0000

Save answer

Question 13 (6 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean μ = 18.6 and standard deviation σ = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will be at least 21 [P( ≥ 21)]?

a. 0.0000

b. 0.3750

c. 0.6250

d. 1.0000

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Question 14 (6 points)

Fortune Magazine reported that the impact of leveraged buyouts is difficult to detect. In 1998 the average value of “Fortune 500” firms who were bought out was $3.75 billion with a standard deviation of $1.92 billion. If a sample of 64 firms is taken from the “Fortune 500” firms, what is the probability that the sample mean is determined to be between $3.5 and $4.5 billion [P($3.5 billion ≤ ≤ $4.5 billion)]?

a. 0.8503

b. 0.8499

c. 0.3503

d. 0.2479

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Question 15 (6 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean μ = 18.6 and standard deviation σ = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will not exceed 17 [P( ≤ 17)]?

a. 0.0000

b. 0.0762

c. 0.9238

d. 1.0000

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Question 16 (10 points)

The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean μ = 18.6 and standard deviation σ = 5.9.

If a random sample of 400 students was drawn, what is the probability that the sample mean () will exceed the norm by at least 2 points [P( – μ ≥ 2)]?

a. 0.0000

b. 0.2513

c. 0.6778

d. 1.0000

Suppose you roll a die. If you roll an odd number, you win the dollar amount corresponding to the number of dots showing. If you roll an even number, you lose the number of dollars corresponding to the number of dots. (For example, if you roll a three you win $3. If you roll a six, you lose $6.) You pay $.50 (fifty cents) to play this game.

a. Find the distribution of the winnings for this game.

b. The amount won is a (discrete, continuous) variable.

c. Find the expected (mean) winnings for this game.

d. Find the standard deviation of the winnings for this game.

e. Suppose you played this game 100 times. Find the mean and standard deviation for the sample mean winnings.

f. The result used in part e. is the ______________________.

20% cars are green; 10 pass by; what is P that 4 are green? Please also provide formula and graph.

Problem:

Complete probability and find the mean and standard dev.

x=250 P(x) = .40

x= 100 P(x) = .10

x= 250 P(x) = .20

x=400

Consider a population of 2000 individuals, 800 of whom are woman. Assume that 300 of the woman in this population earn at least $60,000 per year, and 200 of the men earn at least $60,000 per year.

1. What is the probability that a randomly selected individual from this population earns less than $60,000 per year?

2. If a randomly selected individual is observed to earn less than $60,000 per year, what is the probability that this person is a man?

3. If a randomly selected individual is observed to earn at least $60,000 per year, what is the probability that this person is a woman?

Please use Excel when necessary:

Acording to a recent survey, 70% of all customers will return to the same grocery store.

Suppose 10 customers are selected at random, What is the probability:

a) Exactly 5 of the customers will return?

b) All 10 customers will return?

c) At least 7 of the customers will return?

d) Less than 5 customers will return?

e) How many customers would be expected to return to the same store ?

1, At Acme Inc., women employees are three times as likely to take advantage of computer training courses as men employees. Seventy percent of Acme’s very large work force are women.

a, What proportion of Acme employees who take advantage of computer training courses are women?

b, Twelve percent of the workforce at Acme take computer training courses. What percent of the men employees take computer training courses?

2, a, At a Smith family reunion there are 28 John Smith’s and 18 Jim Smiths in a group photograph. Five of those in the photograph are selected at random. Find the probability that the Johns outnumber the Jims amongst the five chosen.

b, Every time Jim Smith takes his car to the car wash there is a 24% probability that he will forget to retract the radio aerial. Next month he will take his car to the car wash nine times. What is the probability that he will forget to retract the aerial at most four times?

c, What is the mean number of times he will forget to retract, and the standard deviation in the number of times?

3, A time-and-motion-study consultant has been hired at E.I Ltd. She has indentified a certain work station as a bottleneck in production. Initial data suggest that the times required for processing pieces at this station may be treated as having an exponential distribution with a mean of 300 seconds.

a, If 50 pieces are processed, about how many of them take between 240 and 360 seconds to process?

The formula for the cumulative distribution function of the exponential distribution is

b, What is the probability that more than the mean period of pieces will be processed in a ten-minute period?

c, What is the median processing time at the station?

4, The fire department in a city holds fire frills in downtown office buildings. Records show that the times required to evacuate ten-storey buildings during fire drills are approximately normally distributed with a mean of 9 minutes and a standard deviation of 2 minutes. In a one month period 6 randomly selected ten-storey buildings held fire drills.

a, About how many of the buildings were evacuated in less than 8 minutes that month?

B, The fire department wishes to specify a length of time such that ninety-nine percent of ten-storey buildings will be evacuated in that amount of time or less. What length of time should be specified?

Gas Station pump signs, at one chain, encourage customers to have their oil checked, claiming that one out of every four cars should have its oil topped.

a.) What is the probability that exactly 3 of the next 10 cars entering a station should have their oil topped?

b.) What is the probabily that at least half of the next 20 cars entering a station should have their oil topped?

If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, determine the probability that out of 2000 individuals;

a.) Exactly 3

b.) More than 2 individuals will suffer a bad reaction.

Average sale of product is 87,000 on a normal curve with a standard deviation of 4,000. What is the probability that sales will be less than 81,000

The theoretical probability of undesirable side effects resulting from taking Grebex is 1 in 11. If 121 people take Grebex to lower their blood pressure, how many will encounter undesirable side effects?

A multichoice test in which each question has four choices, only one of which is correct. Assume that nine questions are answered by guessing randomly. What is the probability of getting exactly three correct answers.

In one math class of college there aer 10 males and 20 females. The professor makes 3 student teams to work on a group project.

A) How many possible teams can be made?

B) What is a probability that 2 females and 1 male will be in a group?

C) What is a probability of 3 females only?

D) What is a probabilty at least 2 females in a group?

A recent survey reported in Business Week dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money.

CEO Paid More CEO Paid Less

Than $1 Million Than $1 Million Total

Shareholders made money 2 11 13

Shareholders lost money 4 3 7

Total l 6 14 20

If a company is randomly selected from the list of 20 studied, what is the probability?

a. the CEO made more than $1 million?

b. the CEO made more than $1 million or the shareholders lost money?

c. the CEO made more than $1 million given the shareholders lost money?

d. of selecting 2 CEOs and finding they both made more than $1 million?

List the sample space of choosing a ball from a bag containing 2 red balls and 3 black balls.

What is the probability of choosing a queen from a deck of 52 cards? What is the probability of the 2nd card being a queen if the first was a queen? (without replacement)

If we know that P(A) = 3/5; P(B) = 3/5; P(A AND B) = 2/5, then what is P(A OR B)? Are A and B mutually exclusive? Prove your answer mathematically

(a) The 7 letters from the city name, NEW YORK, are put into a bin and drawn out at random without replacement. The letters are arranged from left to right in the order they are drawn. Find the probability that the result spells NEW YORK.

(b) The same experiment as in part (a) above is done with the 7 letters from CHICAGO. Find the probability that the result spells CHICAGO. Is it the same as in part (a)? If so, why? If not, why not?

Super Bowl contender. The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do not play is 1.

What is the probability that San Francisco plays in the next Super Bowl?

The average weekly earnings for women in managerial and professional positions is $685 with a standard deviation of $45. Salaries are normally distributed. Answer the following questions.

a. What is the probability that a woman will have a weekly salary of more than $650?

b. What is the probability that a woman will have a weekly salary of at least $800?

c. For the population, in what range does the middle 95% of weekly salaries lie?

d. If a new sample of 40 women is selected, what is the probability that the mean weekly salary will be between $670 and $705?

e. If new samples of 50 families are selected, what weekly salary to the nearest dollar marks the top 10% of the means of these new samples?

f. If new samples of 100 women are selected, what range of weekly salaries to the nearest dollar marks the 98% confidence interval?

A group of 30 people gather in a room. What is the probability that at least 2 of these people have the same birthday? The year of birth is not considered; having the same birthday means two peple were born on the same day of the year.

Let X be a random variable with uniform distribution over the interval (0,1) and let Y = X^2 (X squared). Find the probability density function of Y.

A rugby team of 13 consists of five backs, six forwards and two halves.

(a) How many teams are possible from a squad of 17, consisting of six backs, eight forwards and three halves?

(b) How many teams are possible from a squad of 17, consisting of six backs, eight forwards and two halves, and one player who could play as a back or a half?

What is probability? How is probability concept used in making business decisions? Please explain with real life examples.

FULL WORKINGS PLEASE.

Clair and Helen frequently play each other in a series of games of table tennis. Records of the outcomes of these games show that whenever they play a series of games, Clair has a probability 0.6 of winning the first game and that in every subsequent game in the series, Clair’s probability of winning the game is 0.7, if he won the preceding game but only 0.5 if he lost the preceding game.

A table tennis game cannot be drawn.

Find the probability that Clair will win the third game in the next series of games played against Helen

If 10% of the people who take a certain drug develop at least one of the side effects. Find the probability that in a sample of 20 people who take the drug:

A. at most one will suffer side effects

b. Exactly four will suffer side effects

c. at least one will suffer side effects

d. all 20 will suffer side effects

Please include formaula.

1. A study shows that employees that begin their work day at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is:

40%

20%

10%

30%

16.7%

2. Suppose that the times required for a cable company to fix cable problems in its customers’ homes are uniformly distributed between 40 minutes and 65 minutes.

What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

.77

.40

.60

.23

3. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

What is the probability that a sheet selected at random will be less than 29.75 inches long?

.8944

.1056

.9332

.0668

4. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

What is the probability that a sheet selected at random from the population is between 29.75 and 30.5 inches long?

.4332

.4878

.0546

.9210

5. During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10.

Find the probability that a household spent less than $5.00.

.9983

0.000

1.00

0.0017

6. During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of $8.22 and a standard deviation of $1.10. What proportion of the households spent between $5.00 and $9.00?

.7611

.7628

.0017

.7594

7. The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. A sample of four metal sheets is randomly selected from a batch. What is the probability that the average length of a sheet is between 30.25 and 30.35 inches long?

.9773

.0227

.0386

.0215

8. The chief chemist for a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.3 ounces of this ingredient from randomly inspected 100 gallons of regular unleaded gasoline?

.5987

.4013

.9938

.0062

9. In the upcoming governor’s election, the most recent poll based on 900 respondents predicts that the incumbent will be reelected with 55% of the votes. For the sake of argument, assume that 51% of the actual voters in the state support the incumbent governor (p = 0.51). Calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor.

.0166

.0247

.0082

.9918

10. According to a hospital administrator, historical records over the past 10 years have shown that 20% of the major surgery patients are dissatisfied with after-surgery care in the hospital. A scientific poll based on 400 hospital patients has just been conducted.

What is the probability that less than 64 patients will not be satisfied with the after-surgery care?

47.72%

2.28%

97.72%

95.44%

4.56%

Over a long period of time, it has been determined that 70% of Lawyers who take the bar examination pass the examination. Of 500 lawyers who take the examination next, find the probability that 330 or fewer will (Question also contained in attachment)

1. For the eight compentecies listed above, what are the means and standard deviations? What two compentencies have the highest means? What two compentencies have the highest standard deviations? Are these what you would expect from vieving the probabilities presented in this table?

2. If 10 business shcools were selected at random what is the probability that at least five of the business school deans agree or strongly agree that improvement in technology and computer usage is crucial to their school recieving accreditaion?

3. Suppose that 20 business schools were selected at random. What is the probability that at least 15 of these schools have deans that agree or strongly agree that improvement in communication skills is crucial to their school receiving accreditation.

4. From question 3 how many business schools would you expect to have deans that agree or stongly agree that improvement in communication skills is crucial to receiving accredidation at their school? What is the standard deviation?

5. For 20 business schools selected from Michigan, suppose it is known that 15 agree or strongly agree that improvement in the global issues competency is crucial to their business school receiving accredidation. If eight of these 20 business schools were selected at random, what is the probability that all eight schools agree or strongly agree that improvement in the global issues competency is crucial to their accreditation.

A company has a turnover of 10% of their hourly employees annually. Thus for any hourly employee chosen at random management estimates a probability of .1 that the person will not be with the company next year.

Choosing three hourly employees at randome use a Tree Diagram and show what is the probability that (1) of them will leave the company this year.

A businessman has an important meeting to attend, but he is running a little late. He can take one route to work that has six stoplights or another, longer route that has two stoplights. He figures that if he stops at more than half of the lights on either route, he will be late for the meeting. Assume independence, and assume that the chance of stopping at each light is p =0.5. Which route should he take?

It is claimed that for a particular lottery, 1/10 of the 50 million tickets will win a prize. What is the probability of winning at least one prize if you purchase (a) 10 tickets or (b) 15 tickets?

BUSINESS ANALYSIS

An urn contains 4 green and 6 blue chips. If the drawing of 2 chips in succession is done with replacement determine the probability of:

A. drawing 2 green chips

B. Drawing a blue chip on the first draw and a green chip on the second draw.

C. Drawing a blue chip on the first draw and a blue chip on the second.

D. Drawing a green chip on the second draw given that a blue chip was drawn on the first draw.

A.. p (green chip) 4/10 x 6/10 = 24/100 p(4) (6) = 24

B. p (blue chip) 6/10 x 4/10 = 24/100 p(6) (4) = 24

C. p (blue chip) 6/10 x6/10 = 36/100 p(6) (6)= 36

D. p (blue chip) 6/10 x 4/10 = 24/100 p(6) (4) = 36

2. An urn contains 3 yellow and 7 blue chips. If the drawing of 2 chips in succession is done without replacing the first chip drawn, determine the probability of:

A. Drawing 2 blue chips.

B. Drawing a yellow chip on the first draw and a blue chip on the second draw.

C. Drawing 2 yellow chips.

D. Drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw.

A. p (blue chip) 7/10 x 6/9 = 42/90 p(7)(6) = 42

B. p (yellow chip) 3/10 x 7/9 = 21/90 p(3)(7) = 21

C. p (yellow chip) 3/10 x 2/9 = 6/90 p(3)(2) = 6

D. p (blue chip) 3/9 x 7/10 = 21/90 P(3)(7) = 21

x + 2x + 8x + 5x + = 1 16x = 1 x = 1/16

3. Our department store is having a sale on personal computers, of which three are in stock (no rain checks). There is a certain probability of selling none. The probability of selling one is twice as great as the probability of selling none. The probability of selling two is four times the probability of selling one. Finally, the probability of selling all the personal computers is five times as great as the probability of selling none. In a table list the outcomes and their probabilities.

QUANTITY DEMAND PROBABILITY

0 x 1/16

1 2x 2/16

2 8x 8/16

3 5x 15/16

p (0) = 0 / 16 x 1/16 = 1/16

p (2) = 0/16 x 2/16 = 2/ 16

p (4) = 2/16 x 4/16 = 8/16

p (3) = 3/16 x 5/16 = 15/16

4. In a production run of 260 units there are exactly 12 defective items.

A. What is the probability that a randomly selected item is defective?

B. If two items are sampled without replacement, what is the probability that both are good?

C. If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective?

A. 12/260 = 0.046 = 5%

B. 12/260 x 12/260 = 144/ 67600 = 0.0021 = 2%

C. 12/260 x 11/259 = 132/ 67340 = 0.0019 = .19

Please see the attached file for full problem description.

—

To determine a target audience for a new email package, a computer company surveyed a large sample of potential customers, asking each whether he or she uses email on a regular basis. (The company considered “a regular basis” to be at least three times a week.) The data, as summarized in the contingency table below, were classified by the age of the respondent and the response to the question.

The respective observed frequencies are written in the cells of the table. In addition, three of the cells have blanks beneath the observed frequencies. Fill in these blanks with the frequencies expected if the two variables, email use and age, are independent.

Round your responses to at least two decimal places.

Under 18 18-35 36-54 55+ Total

On a regular basis 123 109 47 117

(fill this in) 396

Not on a reg. Basis 165 188 51 200

(fill this in) (fillthisin)

Total 288 297 98 317 1000

The “at most” and “at least” topic confuses me

Could you briefly describe both and post a small example to help explain each?

A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labeled A, B, and C. The consumers are classified according to age and package design preference.

A B C Total

Under 25 years 22 34 40 96

25 or older 54 28 22 104

Total 76 62 62 200

If one of these consumers is randomly selected, what is the probability that the person prefers design A and is under 25?

Can anybody help me with this two examples problems. Some of them are giving me a lot of numbers which it should give me a few numbers comparing them to the other results I was manage to do.

————————————————————————————-

2. Social Security Numbers Each social security number is a sequence of nine digits. What is the probability of randomly generating nine digits and getting your social security number?

Positive Test Results Negative Test Result

Subject is pregnant 80 5

Subject is not pregnant 3 11

1. Assume that one of the subjects is randomly selected. Find the probability that the selected subject is not pregnant, given that the test was negative. Is the result the same as the probability of a negative test result given that the selected subject is not pregnant?

Please see the attached file for full problem description.

—

Suppose that a certain college class contains students. Of these, are freshmen, are physics majors, and are neither. A student is selected at random from the class.

a. What is the probability that the student is both a freshman and a physics major?

b. Suppose that we are given the additional information that the student selected is a freshman. What is the probability that she is also a physics major?

Give your answers as exact fractions.

Please see the attached file for full problem description.

—

Suppose that a certain college class contains students. Of these, are sophomores, are chemistry majors, and are neither. A student is selected at random from the class.

a. What is the probability that the student is both a sophomore and a chemistry major?

b. Suppose that we are given the additional information that the student selected is a sophomore. What is the probability that she is also a chemistry major?

Give your answers as exact fractions.

Suppose that A and B are independent events such that P(A)=0.30 and P(B)=0.40.

Find the following probabilities…

(see attachment for full question)

Records of student patients at a dentist’s office concerning fear of visiting the dentist suggest the following proportions: (see attachment for full question).

THE PROBLEM IS ATTACHED AS MICROSOFT WORD.

For two events A and B, the following probabilities are specified.

P (A) = 0.52 P (B) = 0.36 P (AB) =0.20

(a) Enter these probabilities in the following table,

See attached file for full problem description.

A sample space consists of 8 outcomes with the following probabilities.

See attached file for full problem description.

Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule about who will pay the bill: Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yield the same result, the bill will be shared by all. Find the probability that:

a) Only you will have to pay.

b) All three will share.

Of a group of patients 28% visit both a physical Therapist (A) and a chiropractor (B). 8% visit neither. The probability of visiting (A) exceeds the probability of visiting (B) by 16%.

What is the probability of a randomly selected person from this group visiting (A)

According to the US Bureau of Labor Statistics, 75% of the women 25 through 49 years of age participate in the labor force. Suppose 78% of the women in that age group are married. Suppose also that 61% of all women 25 through 49 years of age are married and are participating in the labor force.

a. What is the probability that a randomly selected woman is married or is participating in the labor force?

b. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force but not both?

c. What is the probability that a randomly selected woman in that age group is neither married nor is participating in the labor force?

An investment broker at your brokerage house tells you that he has found a mutual fund that has beaten the S&P market index in 16 of the past 25 weeks. Has he really found a winner or could this be due to chance? What is the probability that this result is due to chance? (By “due to chance,” we mean that there is a 50-50 chance each week that the mutual fund is higher than the S&P market index.) What’s your opinion – winner or just luck?

See the attached file.

1) Let A and B be two events.

a) If the events A and B are mutually exclusive, are A and B always independent? If the answer is no, can they ever be independent? Explain

b) If A is a subset of B, can A and B ever be independent events? Explain

2) Flip an unbiased coin five independent times. Compute the probability of

a) HHTHT

b) THHHT

c) HTHTH

d) Three heads occurring in the five trials.

3) An urn contains two red balls and four white balls. Sample successively five times at random and with replacement, so that the trials are independent. Compute the probability of each of the two sequences WWRWR and RWWWR.

Find the probability for the various situations

1. 5 individuals enter the ground floor of an elevator of a building which has 10 floors(9 floors above the ground floor). Assuming that each of the 5 individuals is going to depart the elevator on one of the 9 floors above the ground floor, (a) what is the probability that all 5 individuals will get o on the same floor? [2]

(b) what is the probability that all 5 individuals will get o on 2 diferent floors? [3]

(c) What is the probability that all 5 individuals will get o on 3 diferent floors? [3]

2. One method of arriving at economic forecasts is to use a consensus approach. A forecast is obtained

from each of a large number of analysts; the average of these individual forecasts is the consensus forecast.

Suppose that the individual 1998 January prime-interest-rate forecasts of all economic analysts are

approximately normally distributed with a mean of 7.1% and a standard deviation of 2.65%. If a single

analyst is randomly selected from among this group, what is the probability that the analyst’s forecast of

the prime interest rate will

(a) exceed 9.85% [4]

(b) 10 analysts from this group are randomly selected. What is the probability that at most 8 of these

analysts forecasted the prime interest rate to be less than 9%. [4]

3. A random variable X having a geometic distribution has the following probability function

P(X = x) = (1 �� p)x��1p: x = 1; 2;

(a) Find MX(t), the moment-generating function of X. [4]

(b) Use your result in (a) to nd the mean of X and the variance of X. [4]

4. A tool and die company makes casting for steel stress-monitoring gauges. Their annual prot, Q (in

$100,000’s), can be expressed as a function of demand (X):

Q(x) = 3(1 �� e��3x):

Suppose the total demand (in 1000’s) for their castings follows the probability distribution with density:

f(x) = 5e��5x for x > 0:

(a) What is the probability that the total demand for castings is between 2000 and 5000? [3]

(b) Find the company’s expected prot. [5]

5. A dice is unbalanced in such a way that the probability of the dice showing i” dots is proportional to

how many dots on the dice1.

Three roommates, Je, Mike, and Wai play a game where this unbalanced dice is tossed until the rst 6

appears. The guy who tosses the rst 6 wins, the prize being that the losers will pay the winner’s portion

of July’s rent. Je, being the oldest, tossess rst, followed by Wai and then Mike. This sequence continues

until the rst 6″ appears.

(a) How many tosses can be expected to occur until the rst 6″ appears? [2]

(b) What is the probability that Je will not have to pay next month’s rent? [6]

1For example, a 6″ is six times as likely as a 1″, a 5″ is ve times as likely as a 1″, etc.

6. Guests arriving at a hotel in accordance with a Poisson process, at a rate of 5 per hour.

(a) What is the probability that no one will arrive in the next hour? [2]

(b) What is the probability that the rst guest will arrive within the rst 10 minutes? [3]

(c) How much time (in minutes) should the hotel expect to pass until the fourth guest arrives from the top

of the hour? Provide a measure of dispersion as well. [3]

7. Let X1;X2; ;Xn be a random sample from a population with a nite mean and a nite variance 2,

with a moment generating function

MXi (t) = e1:5t+3t2

(a) What is the distribution of each Xi [2]

(b) Compute the moment generating function of X =

P10

i=1

Xi

10 and identify the distribution of X. [3]

8. A random sample of size 2 is available from a Poisson distribution with parameter . Let X denote the

sample mean and let Y = (6X1 �� 3X3)=10.

Are Y and X unbiased estimators for ? Is so, which of the two estimators would you recommend. Explain. [8]

James Choi, David Laibson, and Brigitte Madrian conducted an experiment to study the choices made in fund selection. Suppose 100 undergraduate students and 100 MBA students were selected. When presented with four S&P 500 index funds that were identical except for their fees, undergraduate and MBA students chose the funds as follows

Student Group

Fund Undergraduate MBA

Lowest Cost Fund 19 19

Second Lowest Cost Fund 37 40

Third Lowest Cost Fund 17 23

Highest Cost Fund 27 18

If a student is selected at random, what is the probablitiy that he or she

a. Selected the lowest or second lowest cost fund?

b. Selected the lowest cost fund and is an undergraduate

c. Selected the lowest cost fund or is an undergraduate

d. Given that a student is an undergraduate, what is the probability that he or she selected the highest cost fund

e. Do you think undergraduate students and graduate students differ in their fund selection?

The availability of venture capital provided a big boost on funds available to companies recent years. According to Venture Economics, 2,374 venture capital disbursements were made in 1999. Of these 1,334 were to companies in California, 490 were to companies in Massachusetts, 117 were to companies in New York, and 212 were to companies in Colorado. 32% of the companies receiving funds were in the early stages of development a d 45% were in the expansion stage. Suppose you were to randomly choose one of these companies to learn about how they used the funds.

A. What is the probability the company chosen will be in New York

B. What is the probability the company chosen will not be from one of the four states mentioned.

C. What is the probability the company wil not be in the expansion stages of development

D. Assuming the companies in the early stages of development were evenly distributed across the county, how many Massachusetts companies receiving venture capital funds were in there early stages of development.

E. The total amount of funds invested was 32.4 billion. Estimate the amount that went to Colorado.

The Oil Price Information Center reports the mean price per gallon of regular gasoline is 3.26 with a population standard deviation of 0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.

a.) What is the standard error of the mean in this experiment?

b.) What is the probability that the sample mean is between $2.98 and $3.02?

c.) What is the probability that the difference between the sample mean and the population mean is less than 0.01?

d.) What is the likelihood the sample mean is greater than $3.08?

1) A poll states that 30% of the workers in a large company have new desks. If 6 workers are selected at random, what is the probability that at least one worker has a new desk?

2) In a shipment of 20 televisions, 5 are defective. If 2 television sets are randomly selected and tested without replacement, what is the probability that both are defective?

1) In the class, there are 12 freshmen, of whom 8 are males and 15 sophomores, of whom 5 are females. If one student is selected at random, what is the probability of selecting a freshman or a female?

2) In a recent poll by American Automobile Club, 40% of the surveyed said that they were worried about aggressive drivers. If 3 people are randomly selected, what is the probability that all 3 will be worried about aggressive drivers?

3) A Container has 6 blue marbles, 3 red marbles, and 6 white marbles. If 3 marbles are drawn with replacement, what is the probability that all three will be blue?

In order to test a new car, an automobile manufacturer wants to select 4 employees to test drive the car for one year. If 12 management and 8 union employees volunteer to be test drivers and the selection is made at random, what is the probability that at least one union employee is selected?

8. You just bought a new safe: It has a key pad with 26 letters on it. The code is 4 random letters

a. How many different codes are there for you to select from if no letter can be used more than once?

b. If no letter can be used more than once. Does Order Matter?

c. If the manufacturer decided to reduce the code from 4 to 3 (no repeats) how many codes are there then?

d. If letters can be used multiple times (4 inputs), how many different codes are available?

e. If letters can be used multiple times (4 inputs), and the first letter must be an “A” how many different codes are available?

Each of the numbers 1 through 10 inclusive has been written on a separate piece of paper. The 10 pieces of paper have been placed in a hat. If one piece of paper is selected at random, with replacement, find the probability that the number selected is:

a. greater than 3

b. even

c. odd or greater than 3

d. odd or less than 9

In her wallet, Susan has 12 bills. 6 are $1 bills, 2 are $5 bills, 3 are $10 bills, and 1 is a $20 bill. She passes a volunteer seeking donations for the American Red Cross and decides to select 1 bill at random. Determine:

a. probability she selects $ 5 bill (my ans: 1/5)

b. probability she does not select a $5 bill (my ans: 5/6)

c. the odds in favor of her selecting the $5 bill (my ans: 1:5)

d. the odds against her selecting the $5 bill (my ans: 5:1)

e. the odds in favor of her selecting a $10 bill

f. the odds against her selecting a $20 bill

The distribution of blood types for a population are:

40% typeA

9% type B

49% type O

2% type AB

Suppose that the blood types are independent and that both the husband and the wife follow this distribution of blood type.

a) If the wife has type B, what is the probability that the husband has type B?

b) What is the prob that both husband and wife have type B?

c) What is the prob that husband and wife have same blood type?

d) An individual with type B blood can safely receive transfusions only form people with type B or O. What is the probability that the husband of a women with type B blood is an acceptable donor for her?

Brain cancer is a rare disease. In any year there are about 3.1 cases per 100000 od population. Suppose a small medical insurance company has 150000 people on its books. How many claims stemming from brain cancer should the company expect in any year?

What is the probability of getting more than 6 claims related to brain cancer in a year?

Suppose that X is a random variable which can possibly choose 1,2,3,4 with probability P(X=i)=ci, where c is a constant. Find c

Samples of size 49 are drawn from a population with a mean of 36 and a standard deviation of 15. What is the probability that the sample mean is less than 33?

A shipment of 50 VCRs had 6 defectives. If a person bought two cameras, find the probability of getting 2 defectives.

a. .50

b. .10

c. .0122

d. .05

A retail sales worker finds that the probability of making a sale is .23. If she talks to four customer today, what is the probability of her making four sales?

a. 0.003

b. 0.03

c. 0.30

d. 0.001

Please provide explanation and answers to these questions.

1. The Speed master IV automobile gets an average 22.0 miles per gallon in the city. The standard deviation is 3 miles per gallon. Assume the variable is normally distributed. Find the probability that on any given day, the car will get more than 26 miles per gallon when driven in the city. Put answer in decimal form.

2. For a specific year, Americans spent an average of $71.12 for books. Assume the variable is normally distributed. If the standard deviation of the amount spent on books is $8.42, find these probabilities for a randomly selected American. Put answer in percent form.

a. He or she spent more than $60 per year on books.

3. The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend the following amount of time at the exhibit. Assume the variable is normally distributed. Please put in percent form.

a. At least 82 minutes.

4. The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend the following amount of time at the exhibit. Assume the variable is normally distributed. Please put in percent form.

b. At most 50 minutes.

5. The average time a person spends at Barefoot Landing Seaquarium is 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributed. If a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium. Please put answer in decimal form.

a. At least 120 minutes.

6. The average time a person spends at Barefoot Landing Seaquarium is 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributed. If a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium. Please put answer in decimal form.

b. At most 80 minutes.

7. In order to qualify for letter sorting, applicants are given a speed-reading test. The scores are normally distributed with a mean of 80 and a standard deviation of 8. If only the top 15% of the applicants are selected, find the cutoff score. Round to two decimal places.

8. For an educational study, a volunteer must place in the middle 50% on a test. If the mean for the population is 100 and the standard deviation is 15, find the two limits (upper and lower) for the scores that would enable a volunteer to participate in the study. Assume the variable is normally distributed. Round to two decimal places.

9. For a certain group of individuals, the mean hemoglobin level in the blood is 21.0 grams per milliliter (g/ml). The standard deviation is 2 g/ml. If a sample of 25 individuals is selected, find the probability that the mean will be greater than 21.3 g/ml. Assume the variable is normally distributed. Please put you answer in decimal form.

10. The average age of chemical engineers is 37 years with a standard deviation of 4 years. If an engineering firm employs 25 chemical engineers, find the probability that the average age of the group is greater than 38.2 years old. Please put you answer in decimal form.

A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is yellow?

A poll of 1,250 investors conducted, assume that 50% of the investors found the market less attractive to the prior years. P=.5, find the probability that the sample proportion obtained from the sample of 1,250 investors would be:

A. within 4% points of the population, that is P(.46<^p<.54).

B. within 2% points of the population proportion

There are 5 pairs of shoes with distinct size. Now choose any 4 from it randomly, find the probability that they form at least a pair.

1) A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.

A) Compute the probability that a randomly selected household has a savings account.

B) Compute the probability that a randomly selected household has no checking account and no savings account.

C) Compute the probability that a randomly selected household with a savings account has no checking account.

2) A study of Brand M washing machines that failed within three years (warranty period) was 23.2%. Of those that failed, 82.9% lasted over two years. What is the probability that a washer which lasts at least two years will still fail before the end of the warranty period?

3) In an office suite there are three electric typewriters available for personnel to use other than secretaries. Since no one person uses these typewriters, maintenance is not as frequent as for other typewriters. The probability that any one of these typewriters is able to function is 0.90. A mailroom clerk has a form to be filled out and is to type it. It can be typed if any one of the three typewriters operate. Find the probability that at least two of the machines will operate at a given time.

4) New York City is estimated to have 21 percent of the homes with T.V. sets served by cable T.V. If a random sample of four is taken from these homes find the probability distribution of x where x is the number of T.V. homes in the sample having cable T.V. What is the probability that:

a) All four T.V. homes in the sample are served by cable.

b) At least one T.V. home in the sample is served by cable.

c) Compute the mean and standard deviation of the number of T.V. homes with cable service in the sample.

5) In a takeover bid for a certain company, management of the raiding firm believes that the takeover has a 0.65 probability of success if a member of the board of the raided firm resigns, and a 0.30 probability of success if she does not resign. Management of the raiding firm believes that the chances for a resignation of the member in question are 0.70.

a) What is the probability of a successful takeover?

b) Assuming a takeover was not successful, what was the probability that the board member resigned?

6) Which of the following might have resulted from poor sampling design? (Choose only ONE BEST ANSWER)

a. The respondents misrepresented their level of income.

b. The respondents omitted reporting illegal income.

c. The sample failed to include a representative portion of minorities.

d. In a random sample of residents of New York City, 90% of the sample indicated that they were Democrats.

e. The sample was not randomly selected.

I only need help with problems 1, 2, and 3. Please see the following website for the complete problems:http://www.isye.gatech.edu/people/faculty/Robert_Foley/classes/2027/hmwk3.pdf

1. Suppose that the sample space S = {1, 2, 3, …}. Let pk = Pr({k}) for k 2 S. In each of the following

cases, compute c. (a) Suppose that pk = c(5/6)k for k 2 S; (b) Suppose that pk = c(5/6)k/(k)! for

k 2 S.

2. Suppose that the sample space is S = [0,1). Let Bt = [t,1) for any t 0. Suppose that Pr(Bt) =

ce−6t for t 0. Compute (a) c, (b) Pr(B2), and (c) Pr([1, 2)).

3. Suppose we are dealt 6 cards from a standard well-shuffled deck. What is the probability that there

are (a) a six card flush? (b) 4 of one kind and 2 of another? (c) two triples? (d) 3 pairs? (e) 2 pairs?

(f) 1 pair? (g) at least one pair? You may leave your answer in terms of

��n

k

.

A study of 200 grocery chains revealed these incomes after taxes.

incomes after taxes num of firms

under $1million 102

$1 million to 20 million 61

$20 million or more 37

a. What is the probability a particular chain has under $1 million in income after taxes?

b. What is the probability a grocery chain selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? what rule of probability was applied?

In a game at a fraternity party, there are 10 bottles to knock down. Five fraternity brothers line up to shoot the bottles down, each a perfect shot. Each brother selects one bottle at random and shoots. Find the e-value of your distribution of the number of bottles knocked down.

Each brother is a perfect shot so the probability of a brother knocking down their bottle = 1.

The brothers select a bottle at random so more than one brother can target the same bottle.

Mulitple Choice Answers:

a) 3.4

b) 4.1

c) 4.6

d) 5.0

X follows a normal distribution with mean 20 and standrad deviation 4. Find b such that Prob(-b<=X-20<=b)=0.95

1. Business College is planning an online MBA tech program, start up cost for equipment, facilities, course development, staff recruitment and development is $350,000. College plans to charge tuition of $18,000 per student per year. The university administration will charge the college $12,000 per student for the first 100 students enrolled each year for administrative costs and its share of the tuition payments.

How many students does the college need to enroll in the first year to break even?

If the college can enroll 75 students the first year, how much profit will it make?

The college believes it can increase tuition to $24,000, but doing so would reduce enrollment to 35. Should the college consider doing this?

2. Manufacturer discovered 20% of all transmissions installed in particular style truck one year are defective. He contacted the owners of the vehicles and asked that they return the trucks to the dealer to check the transmission. The Auto Mart sold seven of these trucks and has two of the new transmissions in stock. What is the probability that the auto dealer will need to order more new transmissions?

1. Last fall, a gardener planted 65 iris bulbs. She found that only 56 of the bulbs bloomed in the spring.

a) Find the empirical probability that an iris bulb of this type will bloom

b) How many of the bulbs should she plant next fall if she would like at least 92 to bloom?

2. The last 40 violent crimes committed in Sconeville were 2 homicides, 25 robberies, and 13 assaults. What is the empirical probability that the next violent crime committed in Sconeville will be a robbery?

3. One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a spade.

4. The odds against WildHorse winning the third race are 11:2. If Molly places a $4 bet on WildHorse to win and WildHorse wins, find Molly’s net winnings

A) $5.50 B) $44 C) $16.50 D) $11 E) $22

5. 500 raffle tickets are sold at $2 each. One grand prize of $100 and two consolation prizes of $50 will be awarded. Find Jake’s expectation if he purchases one ticket.

A) -$0.40 B) -$1.20 C) -$1.60 D) $7.75 E) $0.80

6. An independent television station airs a movie-of-the-week every Wednesday. Their market research shows that their horror movies are viewed by an average of 2600 people, their comedies are viewed by 4200 people, and their dramas are viewed by 8000 people. The station buys a package of 50 movies, consisting of 5 horror movies, 20 comedies, and 25 dramas. The movies will be shown one per week for 50 weeks. Find the expected number of viewers on a given movie.

A. 5940 B. 5560 C. 4360 D. 6920 D. 5400

7. How many different four-digit numbers can be formed from the digits 0 through 9 if the first digit must be even and cannot be zero?

8. A box of chocolates contains 20 identically shaped chocolates. Five of them are filled with jelly, three are filled with caramel, and twelve are filled with nuts. What is the probability that one chocolate chosen at random is filled with jelly, caramel, or nuts?

9. A couple plans to have exactly three children.

(a) Construct a tree diagram and list the sample space.

(b) Find the probability that the family has at least two girls.

10. (A card is selected from a deck of 52 playing cards. Find the probability of selecting

a) a diamond given the card is black

b) a queen given the card is a picture card.

Find the probability and expected value.

Mr. X invites 15 relatives to a party: his mother, three uncles, two aunts, four brothers, and five cousins. If the chances of any one guest arriving first are equally likely, find the following probabilities:

a. the first guest is an uncle or a cousin

b. the first guest is a brother or a cousin

c. the first guest is an uncle or her mother

An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced and then a second chip is drawn. What is the probability of?

a.) A white chip on the first draw

b.) A white chip on the first draw and a red on the second.

c.) Two green chips being drawn.

d.) A red chip on the second draw given a white chip was drawn on the first.

A class is given a list of 20 study problems from which 10 will be part of an upcoming exam. If a given student knows how to solve 15 of the problems, find the probability that the student will be able to answer,

a. All 10 questions on the exam

b. Exactly 8 questions on the exam

c. At least 9 questions on the exam

An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.

At the first tri-city meeting, there were 8 people from town A, 7 people from town B, and 5 people from town C. If the council consists of 5 people, find the probability of 3 from town A and 2 from town B.

Two distinct even numbers are selected at random from the first ten even numbers greater than zero. What is the probability that the sum is exactly 30?

The Gray Stone Rock Band will give 10 performances this season.Four of these will be only songs from the 70s. If Tony gets to pick two tickets at random, what is the probability that he will get both 70s tickets?

Please indicate whether below statements are True or False? (explain shortly why):

1. If events A and B are independent, then P(A/B) is always equal to zero.

2. If events A and B are mutually exclusive, then P(A/B) is always equal to zero.

3. If the probability of success is 0.4 and the number of trials in a binomial distribution is 150, then its standard deviation is 36.

4. If a fair coin is tossed 100 times, then the variance of the random variable defined as the number of heads is exactly five.

5. If a fair coin is tossed 20 times then the probability of exactly 10 Tails is more than 15 percent.

1) 60% of students are from the south. 60% of them passed the test.

30% are from the north, and 70% of them passed the test.

10% are foreign, and 90% of them passed the test.

If a randomly selected student passed the test, the probability that the student is foreign is_______.

What is the probability of getting three primes in five rolls of a single die?

Assume that 10% of the population is left-handed. If three people are chosen at random, what is the probability that at least one will be left-handed?

1. A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

2. The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated?

(b) Why might a driver be tempted not to use a seat belt “just on this trip”?

One-fourth of the residents of the Burning Ridge Estates leave their garage doors open

when they are away from home. The local chief of police estimates that 5 percent of the

garages with open doors will have something stolen, but only 1 percent of those closed will

have something stolen.

if a garage is robbed, what is the probability the doors were left open?

Problems on moment generating functions

—————————————

1. Let X and Y be independent normal rv’s, each

with mean mu and variance sigma^2. Use moment

generating functions to show that X+Y and X-Y

are independent normal rv’s.

2. If X and Y are independent and

M_X(t)=exp{2e^t-2} and M_Y(t)=(3/4 e^t + 1/4}^{10}.

What is P(XY=0)?

3. Two dice are rolled and X is the sum. Compute M_X.

Problems on limit theorems

————————–

Let Phi(x)=P(Z<x) where Z is the standard normal rv.

Answers to the questions below may be expressed in

terms of the function Phi(x).

4. Treating student test scores as i.i.d., in a

test where the mean is 75 and variance is 25, what

is the probability that a student will score between

65 and 85?

5. Fifty numbers are rounded off to the nearest

integer and then summed. If the individual round-off

errors are independent and uniformly distributed over

(-0.5, 0.5), what is the probability that the resultant

sum differs from the exact sum by more than 3?

6. A die is continually rolled until the total sum

of all rolls exceeds 300. What is the prob that

at least 80 rolls are necessary?

7. Compute P(X>120) for a Poisson rv with mean 100.

Hint: think of X as the sum of 100 independent Poisson

rv’s each with mean 1.

See attached

Use the following to answer questions 20-22:

A $152,400 loan is taken out at 11.5% for 25 years, for the purchase of a house. The loan requires monthly payments.

20. Find the amount of each payment.

21. Determine the total amount repaid over the life of the loan.

22. Find the total interest paid over the life of the loan.

23. In the game Over-and-Under, a pair of dice is rolled and one bets $1 whether the sum of dots showing on the two dice is over 7, under 7, or exactly 7 with payoffs of $2, $2, and $5, respectively. Determine a person’s expected net winnings if the bet is as indicated.

a. Over 7

b. Under 7

c. Exactly 7

d. Is the game fair?

24. A box contains 4 defective and 8 good light bulbs. If 3 bulbs are selected at random. What is the probability that exactly one is good?

25. Four percent of the items coming off an assembly line are defective. If the defective items occur randomly and ten items are chosen for inspection, what is the probability that exactly two items are defective?

26. The following data represent the number of car accidents per month in a small town over a two-year period.

Number of Accidents

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec -1

Yr 1 169 163 170 165 165 169 168 172 170 172 171 165 -1

Yr 2 170 168 177 164 173 166 173 176 177 172 170 172 -1

Construct a frequency distribution based on the intervals 163 – 165, 166 – 168, 169 – 171, 172 – 174, 175 – 177.

Use the following to answer questions 27-31:

Use the following sample: 28, 30, 24, 30, 32, 40, 22, 25, 26, 34

27. Find the mean.

28. Find the median.

29. Find the mode.

30. Find the standard deviation for a sample.

31. Find the z-score for 30. (Assume a normal distribution.)

32. A probability distribution has an expected value of 28 and a standard deviation of 4. Find the area under the standard normal curve between 20 and 36

Use the following to answer questions 33-34:

Using z-scores, what is the area under the standard normal curve?

33. To the left of 1.8?

34. Between 2.20 and 1.36

Please show all steps for clarification.

Find the probability that the 2-card hand described above contains the following:

1. Two aces

2. At least one ace

3. All spades

I need some step-by-step help for the following three basic problems.

1. A group of 8 professors and 5 administrators must select a team of 6 people from the group. They decide to select the team members randomly by drawing names from a hat. What is the probability that the selected team will consist of equal numbers of professors and administrators (3 of each)?

2. If you roll a single die 120 times, approximately how many times should you expect the number 5 to come up? Is the answer 1/6th of the time or 20 times?

3. In a certain craps game at a casino, if you place a bet on the “4”, and a 4 comes up on a roll of the two dice before a 7 comes up, the payout odds are 9 to 5. Convert these odds to the player’s win probability.

A jar contains 2 orange jellybeans, 6 red jellybeans, 6 green jellybeans and 4 yellow jellybeans. You pick a jellybean without looking.

a). What is the probability that it is orange?

b). What is the probability that it is orange, given it is NOT red?

c). What is the probability of picking yellow or green?

#1.) Dr.Radman has been collecting data on a simplified intake form. One measure that was taken was the amount of time (in minutes) it took people to complete this form. The time to complete the simplified form was Mean=22 minutes and Standard Deviation= 3 minutes (assume there were enough forms completed to justify using population parameters). Dr. Radman has randomly selected some scores and wants to transform them to the time it would have taken to complete the original form. That version had a Mean=50 minutes and a Standard Deviation=10 minutes. Transform the times for the simplified score completion times so they would correspond to the original form completion times for Dr.Radman. Simplified form times: 20,17,28.

#2.) You are the supervisor of your department and have just received the rankings for your department. however, the report failed to include the mean and standard deviation for your entire workplace. You really want to know more information about the distribution for the general workplace. The report indicates that a score of X=65 corresponds to a z-score of a=+2.00, and a score of X=44 corresponds to a z-score of z=-1.50.

a.) indicate the mean and standard deviation for this distribution.

b.) If your department received a z-score of 2.50, indicate the score your department received.

c.) You are going to determine the probability of your department achieving this score, what assumptions do you have to make about this distribution?

d.) Indicate the probability of your department achieving that score and explain what this score indicates about your department rating.

[1] On a recent English test, students were given the names of four authors and four novels (one author one title), and asked to match each novel, with the correct author. If a student just guesses randomly, what is the probability of getting zero, one, two, three or four correct?

[2] You are to select two cards one at a time from a well-shuffled deck of 52 playing cards (jokers not allowed). You want to get a heart as the first card and a King (K) as the second.

If you are given the following two options to do this, which option would you choose,

Option #1: to be allowed to select the first card and put it back into the deck before selecting the second card, or

Option #2: to be allowed to keep the first card (not to put it back to the deck) and select the second one?

a) Explain why you think your choice is better.

b) What is the probability to select such two cards under option #1?

c) What is the probability to select such two cards under option #2?

d) Does your choice from a) agree with the results from b) and c)? Explain.

I have two pair of black shoes in the closet, a loafer and a tied pair. I am in a hurry getting dressed and the light burns out in the closet. As these are the only shoes in the closet, I reach in and grab two.

What is the probability that they match (i.e. l and r loafer, or l and r tie – wearing a tie and a loafer is a fashion faux pas)?

Am I justified in making a pick in the dark, or should I have taken the time to get a new light bulb?

Market Researchers, Inc. has been hired to perform a study to determine if the market for a new product will be good or poor. In similar studies performed in the past, whenever the market actually was good, the market research study indicated that it would be good for 85% of the time. On the other hand, whenever the market actually was poor, the market study incorrectly predicted it would be good 20% of the time. Before the study is performed, it is believed there is a 70% chance the market will be good. When Market Researchers, Inc. performs the study for this product, the results predict the market will be good. Given the results of the study, what is the probability that the market will be good?

The Springfield Kings (a professional basketball team), has won 12 of its last 20 games and is expected to continue winning at the same percentage rate. The team’s ticket manager is anxious to attract a large crowd to tomorrow’s game but believes that depends on how well the Kings perform tonight against the Galveston Comets. He assesses the probability of drawing a large crowd to be .90 should the team win tonight. What is the probability that the team wins tonight and that there will be a large crowd at tomorrow’s game?

See attached

A flu vaccine has a probability of 80% of preventing a person who is inoculated from getting the flu….

Consider a seven-game world series between team A and B, where for each game

P(A wins)=0.6

a) Find P(A wins series in x game)

b) You hold a ticket for the seventh game. What is the probability that you will get to use it? .answer 0.2765

c) if P(A wins a game)=p, what value of p maximizes your chance in b)?answer p=1/2

d) what is the most likely number of games to be played in the series for p=0.6?

answer x=6

I have the answer but I do not understand the process. Can you explain this with details and step by step What does most likely means?

(27) A company is in the process of hiring new employees for its sales force. The Human Resource manager estimates that the following are the probabilities of how many sales people will be hired during the next three months:

No. To Be Hired Probability

0 5%

1 10%

2 20%

3 20%

4 25%

5 10%

6 10%

What is the expected number of new hires over the next three months?

a. 3.4

b. 3.1

c. 2.9

d. 3.2

e. None of the above

(28) In question #27, what is the expected range of new hires over the next three months with approximately 75% probability?

a. 0 to 6.4 persons

b. .4 to 4.2 persons

c. 1.2 to 4.4 persons

d. 1.6 to 5.4 persons

e. None of the above

(37) A cola dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liters. What is the probability a container will have more than 2 liters?

a. 0.0918

b. 0.1327

c. 0.8673

d. 0.9082

e. None of the above

(36) Elly’s hot dog emporium is famous for chili dogs. Some customers order hot dogs with hot peppers, while many do not care for the extra zest. Elly’s latest taste test indicates that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that between 2 and 6 customers inclusive want hot peppers?

a. 0.504

b. 0.645

c. 0.708

d. 0.785

e. None of the above

(30) A personnel officer has 12 candidates to fill five positions. Assuming any candidate can fill any of the positions, what is the possible number of ways to fill the positions??

a. 550

b. 792

c. 4,636

d. 95,040

e. None of the above

1.You randomly choose an integer from 0 to 9; what are the odds that the integer is 3 or more?

2.You toss 3 coins, what’s the probability that all are heads?

3.Order these numbers in an increasing order:

–>1.5,NEGATIVE 2.4, 2.1, NEGATIVE 1.6, 3.3

–>2 AND 5 NINTHS,2.5,NEGATIVE 1.25, NEGATIVE ONE FIFTH, NEGATIVE 1 AND 2 NINTHS

A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said they were planning to vote for the current mayor. Based on this sample, what is your initial hunch? If you calculated the 95% confidence interval around the mayorâ??s current proportion of votes, would you claim with 95% confidence that the mayor will win a majority of the votes if the election were held today? Explain

Problem 5. An airline tracks data on its flight arrivals. Over the past six months, 65 flights on one route arrived early, 273 arrived on time, 218 were late, and 44 were cancelled

? a. What is the probability that a flight is early? On time? Late? Cancelled?

? b. Are these outcomes mutually exclusive?

? c. What is the probability that a flight is either early or on time?

Problem 6. A survey of 100 MBA students found that 60 owned mutual funds, 40 owned stocks, and 20 owned both.

? a. What is the probability that a student owns a stock? A mutual fund?

? b. What is the probability that a student owns neither stocks nor mutual funds?

? c. What is the probability that a student owns either a stock or a mutual fund?

Problem 8. The weekly demand of a slow-moving product has the probability mass function:

Demand, x Probability, f(x)

0 0.1

1 0.4

2 0.3

3 0.2

4 or more 0

Find the expected value, variance, and standard deviation of weekly demand.

Medical studies have shown that 10 out of 100 adults have heart disease. When a person with heart disease is given an EKG test, a 0.9 probability exists that the test will indicate the presence of heart disease. When a person without heart disease is given an EKG test, a 0.95 probability exists that the test will indicate the person does not have heart disease. Suppose that a person arrives at an emergency room com-plaining of chest pains. An EKG is given and indicates that the person has heart dis-ease. What is the probability that the person actually has heart disease?

Problem 3:

Suppose that a batch of 100 items contains 6 that are defective and 94 that are nondefective. If X is the number of defective items in a randomly drawn sample of 10 items from the batch, find

a) P(X = 0)

b) P(X > 2)

Problem 2:

An army is composed of 5 divisions. Each division has 10,000 soliders. In each regiment the desertion rate is 2 soldiers per month. DESERTERS ARE REPLACED.

a) Find the probability that in the army as a whole there will be 3 or more desertions in a given month.

b) What is the probability that there will be at least 3 months during the year that will have 2 or less deserters.

As reported by Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Let X be the finishing time for a finisher in the New York 10-km run.

a) What is the chance that finishers complete the run with the times between 50 and 70 minutes?

b) What is the chance that finishers complete the run with the times more than 75 minutes?

c) How fast do finishers have to complete the run among the top 5% finishers?

Probability

In Excel

1. According to Investment Digest (“Diversification and the Risk/Reward Relationship”, Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 19.4%, and the standard deviation of the annual return was 24.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.

Find the probability that the return for common stocks will be greater than 8%.

Find the probability that the return for common stocks will be greater than 20%.

Hint: There are many ways to attack this problem in the HW. If you would like the normal distribution table so you can draw the pictures (my preferred way of learning) then I suggest you bookmark this site:

http://www.statsoft.com/textbook/sttable.html

Confidence Interval Estimation

2. Compute a 90% confidence interval for the population mean, based on the sample 25, 27, 23, 24, 25, 24, and 59. Change the number from 59 to 24 and recalculate the confidence interval. Using the results, describe the effect of an outlier or extreme value on the confidence interval.

Hypothesis Testing

3. The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the university indicates that X (bar) = $285.4 and s = $42.20.

a. a. Using the 0.05 level of significance, is there evidence that the population mean is above $300?

b. b. What is your answer in (a) if s = $90 and the 0.10 level of significance is used?

c. c. What is your answer in (a) if X (bar) = $310.10 and s = $40.20?

d. d. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

4. A large hat manufacturer, MICHAELLA HATS, is concerned that the mean weight of their signature Kentucky Derby hat is not greater than 3.5 pounds. It can be assumed that the population standard deviation is .7 pounds based on past experience. A sample of 350 hats is selected and the sample mean is 3.25 pounds. Using a level of significance of .10, is there evidence that the population mean weight of the hats is greater than 3.5 pounds? Fully explain your answer.

Please see the formula sheet and standard normal distribution table to be used.

Only use a scientific or graphing calculator (Excel does not help me) and please show all working out.

Question 8

A recent study showed that 75% of all people over 60 years of age wear eye glasses. If a random sample of five persons over the age of 60 is selected, what is the probability that

a. none of the five wear eye glasses?

b. at most two of the five wear eye glasses?

Question 9

Waiting times to receive service at a popular fast-food restaurant during the early morning rush period are approximately normally distributed with a mean of 3.5 minutes and a standard deviation of 1.5 minutes.

a. What is the probability that a randomly selected customer has to wait exactly three minutes?

b. What is the probability that a randomly selected customer will have to wait between 4.25 and 5.375 minutes?

c. Seventy-five percent of customers will wait less than what amount of time to receive service?

Question 10

The failure rate on a driver’s test is 25%. If 200 people take the test, what is the probability

a. that 60 or more will fail the test?

b. that exactly 40 will fail the test?

66. Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at the graduation.

a. What is the probability both of the selected students plan to attend college?

1. P (A) + P (B) =

b. What is the probability one of the two selected students plans to attend college?

1. P (A) + P (B) =

Jason must decide how many cases of cheese to manufacture each month. The probability that the demand will be 6 cases is 0.1, for 7 cases is 0.3, for 8 cases is 0.5, and for 9 cases is 0.1. The cost of each case is $45 and the price Jason gets for each case is $95. Any case not sold by the end of the month is of no value due to spoilage. How many case of cheese should Jason manufacture each month?

An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be

(a) the same color

(b) different colors

A study of college football games shows that the number of holding penalties assessed has a mean of 2.2 penalties per game and a standard deviation of 0.8 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.05 penalties per game or less?

If A and B are independent events with P(A) = 0.25 and P(B) = 0.60, then P(A/B) is?

2. Intentions of customers regarding future automobile purchases and the financial capability of the consumers are given below:

Plan to buy

qualify for within 6 6 months or No

financing months (A) longer (B) (C)

Yes (D) 0.30 0.20 0.10

No (E) 0.10 010 0.20

What is the probability of P(A/D)?

The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than $6.75?

Answer rounded to 4 decimal places.

A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces:

Exactly 5 will be defective?

5 or more will be defective?

Problem #1

Dr. Stallter has been teaching basic statistics for many years. She knows that 80 percent of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90 percent will pass the course. Among those students who do not do their homework, 60 percent will pass. Mike Fishbaugh took statistics last semester from Dr. Stallter and received a passing grade. What is the probability that he completed the assignments?

Problem #2

One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 percent of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If a garage is robbed, what is the probability the doors were left open?

In a class of 10 students, what is the probability that at least 2 students were born on the same day of the year (365 days)?

1. P(A1) = .20, P(A2) = .40, and P(A2) = .40. P(B1|A2) = .25. P(B1|A2) = .05, and P(B1|A3) =.10. Use Bayes’ theorem to determine P(A3 | B1).

2. Dr. Stallter has been teaching basic statistics for many years. She knows that 80 percent of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90 percent will pass the course. Among those students who do not do their homework, 60 percent will pass. Mike Fishbaugh took statistics last semester from Dr. Stallter and received a passing grade. What is the probability that he completed the assignments?

3. One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 percent of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. If a garage is robbed, what is the probability the doors were left open?

A well known apple juice production company maintains records concerning the number of unacceptable containers of apple juice obtained from the filling and capping machines. Based on past data, the probability that a container came from machine I and was nonconforming is 0.03 and the probability that a container came from machine II and was nonconforming is 0.07. These probabilities represent the probability of one container out of the total sample having the specified characteristics. Half the containers are filled on machine I and the other half are filled on machine II.

a. If a filled container of juice is selected at random, what is the probability that it is a nonconforming container?

b. If a filled container of juice is selected at random, what is the probability that it was filled on machine II?

c. If a filled container of juice is selected at random, what is the probability that it was filled on machine I and is a conforming container?

1. A study of a court system produced the following results:

Note: G= guilty , G’ = not guilty , J= judged guilty , J’= judged not guilty

80% of guilty (G) judged guilty (J)

93% of innocent (G’) judged innocent (J’)

5% innocent (G’) judged guilty (J)

77% guilty (G)

A) Find probability judged guilty (means find P(J))

B) Find probability of innocent if judged guilty

Answers: Just show me how to get here.

A) 62.8%

B) 1.8%

2. A large industrial firm uses 3 hotels which sometimes have bad plumbing

PL’ = bad plumbing H= hotel

P(H) PL’

Ramada 41% 2%

Sheraton 33% 7%

Lakeview 26% 6%

A) What is the probability a client randomly assigned a hotel will have bad plumbing in his or her room?

B) Probability a guest stayed at Lakeview if his room had bad plumbing?

Answers: Again, just show me.

A) 4.7%

B) 33%

1. A real estate agent is taking potential buyers to look at 7 houses for sale. She has a key for each house, but she brough only 4 of the keys with her. Not all of the houses are locked. In fact, 25% are not locked. She has taken the potential buyers to the first house and will try to get them through the door. What is the probability that she will be successful?

2. A town has two fire trucks, A and B. They are operated independently. Given that the probability the fire truck A will arrive in 10 minutes of a call is 81% and that the probability the fire truck B will arrive within 10 minutes of a call is 93%

A) What is the probability that neither truck will be there within 10 minutes?

B) What is the probability that at least one of the two truck will be there in time?

I just wanted help to set up the problem and what-not, the professor gave the answers its just our part to figure out how it goes together.

Answers:

1) 67.9%

2) a) 1.3%

b) 98.7%

Consider the following contingency table:

Under 20 21-30 31-40

Male 12 12 17

Female 13 16 21

a. If one person is selected at random, what is the probability that person is Female? ______

b. If one person is selected at random, what is the probability that person is either under 20 or over 30? _______

c. If one person is selected at random, what is the probability that person is either male or in the age group 21-30? _____

d. If two people are selected at random, what is the probability they are both female? ______

The population of diameter widths of steel rebar is normally distributed with a mean of 2.5cm and a standard deviation of 0.25cm.

What is the probability that the average diameter width of a strip of rebar from a sample of 23 strips is more than 2.6cm wide?

Attached is a copy of an Excel spread sheet,

?This spreadsheet contains 4 worksheets

oWorksheet #1: Lists the random numbers you use for your simulation. There are three sets, with each set having up to 50 numbers. Use each set for each type of randomization. For example, on problem 9, you will use the first set to randomize interarrival times and the second set to randomize service times.

oWorksheet #2: This contains the solution to problem 4-12. The formulas contained in this worksheet should assist you with 4-9 and 4-20. Also note how the random numbers from worksheet #1 were used in this worksheet.

oWorksheet #3: Contains problem 4-9, to complete

oWorksheet #4: Contains problem 4-20, to complete.

Problem 12 is already done. their are only two problems that is 9 and 20

See the attached file.

Jan’s big brown dog Shtutzy has recently learned how to open the fridge. One day Jan leaves a dozen (12) eggs in the fridge. Two of the eggs are rotten. the rest are good. When Jan comes home, the fridge is ransacked. Among other things, Shtutzy ate 5 eggs out of the dozen. Assume that she picked the eggs at random without any attention to whether the eggs are good or not. (Note: Binomial coefficients need NOT be evaluated in the followings.)

(a) What is the probability that Shtutzy ate the two rotten eggs?

(b) Shtutuzy is known to have a “stomach of steel”. If she eats one rotten egg, she will be sick with probability 0.2. If she eats two rotten eggs, she will be sick with probability 0.5. If she does not eat any rotten egg. She will still be sick with probabilIty 0.01 from eating too much. What is the chance that Shtutzy will be sick?

(c) I have a good news: Shtutzy is not sick. Given this information, find the probahility that Shtutzy ate the two rotten eggs.

1. A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.

a. Assuming the company’s claim is true, if one home is selected at random, what is the probability that it will be sold in less than 63 days?

b. Assuming the company’s claim is true, if a random sample of 9 homes is selected, what is the probability that the mean selling time will be less than 63 days?

c. Assuming the company’s claim is true, if a random sample of 64 homes is selected, there is a 75% probability that the sample mean is greater than how many days?

d. Do you have to know that selling times are normally distributed to answer part (c)? Explain why or why not.

Suppose you doubt the companyâ??s claim that their average selling time is 57 days. To test their claim, you select a random sample of 64 homes and the sample mean number of days to sell those homes is 62 days. Do you have evidence to refute the companyâ??s claim? Explain why or why not

See attached file for formulas.

2. Based on FAA estimates the average age of the fleets of the ten largest U.S. commercial passenger carriers is 13.4 years with a standard deviation of 1.7 years. Suppose that 40 airplanes were randomly selected from the fleets of these ten carriers and were inspected for cracks in the airplanes that are considered too large for flying. What is the probability that the average age of these 40 airplanes is at least 14 years old?

[use the following formula to get the z-value: where, is the sample, µ is the population mean, ‘s’ is the sample standard deviation, and ‘n’ is the sample size]. Use the z-value to find the probability value in the standard normal table. Keep in mind that ‘at least’ show a cumulative probability.

3. Roxanne is a frequent business traveler, going back and forth from LA to Chicago several times per month. To catch her flights from LA she leaves her office one hour before her flight leaves. Her travel time from her office to the departing gate at LA airport includes driving to the airport, parking, check-in, and passing the security checking. The travel time is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. A) what is the probability that Roxanne will miss her flight when her travel time from office to the LA airport exceeds one hour?

[use probability, probability & probability distributions, normal in Phstat or use probability, continuous probability in Megastat].

Please see the attached JPEG for homework specifics.

If x and y are discrete random variables with a joint pdf of…

12.) The following table shows the weather conditions each day for the last 100 days:

Snowy Days

Snowy Days Rainy Days Cloudy Days Sunny Days

5 20 40 35

Based on this data:

a.) What is the probability that tomorrow will be snowy?

b.) What is the probability that tomorrow will be rainy or cloudy?

c.) What is the probability that tomorrow will be rainy and the day after tomorrow will be sunny?

13.) The probability of a newborn baby being a girl is 0.49. If four babies are born in a hospital on one day, what is the probability that all four are girls?

1. Of 23 college sophomores at Crocodile Community College, 12 preferred pepperoni pizza, 7 preferred supreme, and 4 preferred cheese. If we picked a college sophomore at Crocodile Community College at random, what is the probability that he or she would prefer supreme? Give solution exactly in reduced fraction form.

2. If the probability of seeing moose in a day in a certain region of Alaska is 0.29, what is the probability of not seeing any moose in a day there?

3. If the odds of winning a raffle are 7:229, what is the probability of winning?

4. According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

U. S. State 2008 Population

Missouri 5,911,605

Pennsylvania 12,448,279

Tennessee 6,214,888

Utah 2,736,424

Washington 6,549,224

SOURCE: U. S. Census Bureau

What is the probability that a randomly selected U.S. resident did not live in Missouri? Show step by step work. Round solution to the nearest thousandth.

5. A simple dartboard has three areas… the main board has a radius of 10 inches, there is a circle with a radius of 7 inches, and the bullseye has a radius of 3 inches. What is the probability of a random dart landing inside the bullseye?

6. A certain drawing states that the odds of winning are 15:270. What would be the odds against winning?

7. The property restoration company PuroServ is considering switching to new dehumidifiers. Their market research, considering the cost of the new machines and their efficiency, tells them that the switch would give them a 72% chance of making a $20,000 profit, a 14% chance of breaking even, and a 14% chance of losing $5,000. How much money does PuroServ expect to make with their new purchase?

8. Last fall, a gardener planted 55 iris bulbs. She found that only 45 of the bulbs bloomed in the spring.

a. Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.

b. How many of the bulbs should she plant next fall if she would like at least 51 to bloom?

9. A community 5K run will award $50 to the winner. 55 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.

A recent report in Business Week indicated that 20 percent of all employees steal from their company each year.

If a company employs 50 people, what is the probability that:

a. Fewer than 5 employees steal?

b. More than 5 employees steal?

c. Exactly 5 employees steal?

d. More than 5 but fewer than 15 employees steal?

1.Sixyy nine percent of adults favor gun licensing in general. Choose one adult at random. What is the probability that the selected adult doesn’t believe in gun licensing?

2.In a recent year, of the 1,184,000 bachelor’s degrees conferred, 233,000 were in the field of business, 125,000 were in the social sciences, and 106,000 were in education. If one degree is selected at random, find the following probabilities.

a. That the degree was awarded in education.

b. That the degree was not awarded in business.

3.In a survey, 16 percent of American children said they use flattery to get their parents to buy them things. If a child is selected at random, find the probability that the child said he or she does not use parental flattery.

4.The source of federal government revenue for a specific year is

50% from individual income taxes

32% from social insurance payroll taxes

10% from corporate income taxes

3% from excise taxes

5% other

If revenue is selected at random, what is the probability that it comes from individual or corporate income taxes?

5.At a used book sale, 100 books are adult books and 160 books are children’s books. Seventy of the adult books are nonfiction while 60 of the children’s books are nonfiction. If a book is selected at random, find the probability of selecting the following

a. fiction

b. not a children’s nonfiction

c. an adult book or a children’s nonfiction

6. This distribution represents the length of time a patient spends in a hospital

Days Frequency

0-3 2

4-7 15

8-11 8

12-15 6

16+ 9

If a patient is selected, find these probabilities

a.the patient spends 3 days or fewer in the hospital

b.the patient spends fewer than 8 days in the hospital

c.the patient spends 16 or more days in the hospital

d.the patient spends a maximum of 11 days in the hospital

7. If one half of Americans believe that the federal government should take primary responsibility for eliminating poverty, find the probability that three randomly selected Americans will agree that it is the federal governments responsibility to eliminate poverty.

8. A circuit to run a model railroad has eight switches. Two are defective. If a person selects two switches at random and tests them, find the probability that the second one is defective, given that the first one is defective.

9. A lot of portable radios contains 15 good radios and 3 defective ones. If two are selected and tested, find the probability that at least one will be defective.

10. A medication is 75% effective against a bacterial infection. Find the probability that if 12 people take the medication, at least one person’s infection will not improve.

Textbook authors and publishers work very hard to minimize the number of errors in a text. However, some errors are unavoidable. Mr. J. A. Carmen, statistics editor, reports that the mean number of errors per chapter is 0.8. What is the probability that there are less than 2 errors in a particular chapter?

A normal distribution has a mean of 50 and a standard deviation of 4.

a-compute the probability of a value between 44.0 and 55.0.

b-compute the probability of a value greater than 55.0.

c-compute the probability of a value between 52.0 and 55.0

A survey of grocery stores in the Southeast revealed 40 percent had a pharmacy, 50 percent had a floral shop, and 70 percent had a deli. Suppose 10 percent of the stores have all three departments, 30 percent have both a pharmacy and a deli, 25 percent have both a floral shop and deli, and 20 percent have both a pharmacy and

floral shop.

a. What is the probability of selecting a store at random and finding it has both a pharmacy and a floral shop?

b. What is the probability of selecting a store at random and finding it has both a pharmacy and a deli?

c. Are the events ‘select a store with a deli’ and ‘select a store with a pharmacy’ mutually exclusive?

d. What is the name given to the event of ‘selecting a store with a pharmacy, a floral shop, and a deli?’

e. What is the probability of selecting a store that does not have all three departments?

Probability: Mary is taking two courses, photography and economics. Student records indicate that the probability of passing photography is 0.75, that of failing economics is 0.65, and that of passing at least on of the two courses is 0.85. Find the probability of the following: a.Mary will pass economics. b. Mary will pass both courses. c. Mary will fail both courses. d. Mary will pass exactly one course.

An automatic machine inserts mixed vegetables into a plastic bag. Past experience shows that some packages were underweight and some were overweight, but most of them had satisfactory weight.

Weight Percentage of Total

Underweight 2.5

Satisfactory 90.0

Overweight 7.5

a) What is the probability of selecting and finding that all three bags are overweight?

b) What is the probability of selecting and finding that all three bags are satisfactory?

1. In a bag there are 2 red, 3 yellow, 4 green, and 6 blue marbles.

What is the probability of P (yellow or green)?

Choose the best answer from the options below:

A 6 / 10

B 7 / 15

C 3 / 10

D 2 / 15

2. A spinner has the numbers 1 thru 9. The spinner is spun once.

What is the probability of P (3, 6 or 8)? Write the answer as a percent.

Choose the best answer from the options below:

A 30%

B 40%

C 33.33%

D 100%

3. A spinner has the numbers 1 thru 9.

What is the probability of P(less than 6)? Write the answer as a decimal.

Choose the best answer from the options below:

A 0.222

B 0.333

C 0.444

D 0.555

Cruise ships of the Royal Viking line report that 80 percent of their rooms are occupied during September. For a cruise ship having 800 rooms, what is the probability that 665 or more are occupied in September?

Consider a comp. that selects employees of ramdom data drug test. the comp. uses a computer to select randomly employees # that range from 1 thru 6873.

probability of selecting a # < 500.

Among U.S. cities with a population of more than 250,000 the mean one-way commute to work is 24.3 minutes. The longest one-way travel time is New York City, where the mean time is 37.9 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 6.9 minutes.

(a) What percent of the New York City commutes are for less than 29 minutes?

(b) What percent are between 29 and 35 minutes?

(c) What percent are between 29 and 42 minutes?

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $2,020. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $456. (Round z-score computation to 2 decimal places and your final answer to 2 decimal places. Omit the “%” sign in your response.)

(a) What percent of the adults spend more than $2,600 per year on reading and entertainment?

(b) What percent spend between $2,600 and $2,900 per year on reading and entertainment?

(c) What percent spend less than $1,200 per year on reading and entertainment?

A ball is picked at random from a box containing 3 white, 5 red, 8 blue and 7 green balls. Find the probability a blue ball is picked.

Mary is taking courses in both Reading and English. She estimates her probability of passing Reading of 0.4 and English at 0.6 and she estimates her probability of passing at least one of them at 0.8. What is her probability of passing both courses?

A TV show, DOG and CAT, recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to that show. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 9 households having TV sets in use at the time of a GOD and CAT broadcast:

– Find the probability that none of the households are tuned to DOG and CAT _____ (round to three decimal places as needed)

– Find the probability that at least one house hold is tuned to DOG and CAT ____ (do not round until final answer. Then round to three decimal places as needed)

– Find the probability that at most one household is tuned to DOG and CAT ____ (do not round until final answer. Then round to three decimal places as needed)

– If at most one household is tuned to DOG and CAT, does it appear that the 20% share value is wrong?

a. YES because the 20% rate, the probability of at most one household is greater than .05

b. YES because the 20% rate, the probability of at most one household is less than .05

c. NO because the 20% rate, the probability of at most one household is less than .05

d. NO because the 20% rate, the probability of at most one household is greater than .05

In a region, 20% of the population has brown eyes. If 15 people are randomly selected, find the probability that at least 13 of them have brown eyes. Is it unusual to randomly select 15 people and find that at least 13 of them have brown eyes?

– The probability at least 13 of 15 have brown eyes = ____ (three decimal places as needed)

– Is it unusual to randomly select 15 people and find that at least 13 of them have brown eyes? Note that a small probability is one that is less than .05.

a – NO, because the probability of this occurring is not small

b- YES, because the probability of this occurring is very small

c- NO, because the probability of this occurring is very small

d- YES, because the probability of this occurring is not small

Please send detailed solutions in 2 hours.

1. You have grown soybeans for 40 years, and have experienced 5 crop failures in that time period. What is the probability of a crop failure in any given year?

2. Based on the annual probability of crop failure you found in question 1, what is the expected number of crop failures in the next 40 years?

3. You have two chicken houses: red and green. Forty thousand chickens are in the red house and 60 thousand are in the green house. Five percent of the chickens in the red house have hookworm, while only 2% of the chickens in the green house are infected.

(a) What is the probability that a randomly selected chicken is from the green house?

(b) What is the probability that a randomly selected chicken has hookworm?

(c) Given a randomly selected chicken has hookworm, what is the probability it is from the red house?

The Senate consists off 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.

If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg:

1. Construct a similar sample space for the possible gender outcomes (using b for boy a g for girl) of two children?

2. Assuming that the outcomes listed in part 1 were equally likely, find the probability of getting two boy children?

3. Find the probability of getting exactly one boy child and one girl child?

1. A lady has six cats. Each cat has a 0.60 probability of climbing into the chair in which the lady is sitting, independently of how many cats are already in the chair with the lady. Find the probability distribution for the number of cats in the chair with the lady. Find the expected number of cats in the chair with the lady.

1. An economist wishes to estimate the average family income in a certain population. The population standard deviation is known to be $4,500, and the economist uses a random sample of size = 225.

a. What is the probability that the sample mean will fall within $800 of the population mean?

b. What is the probability that the sample mean will exceed the population mean by more than $600.

Please provide full detail including how the z-table lookup is determined.

2. The article “Reliability of Domestic Waste Biofilm Reactors” (J. of Envir. Engr., 1995: 785-790) suggests that substrate concentration (mg/cm^3) of influent to a reactor is normally distributed with  = 0.30 and  = 0.06.

a. What is the probability that the concentration exceeds 0.40?

b. What is the probability that the concentration is at most 0.25?

c. How would you characterize the largest 10% of all concentration levels?

Please provide full detail.

Given that 2 of 211 subjects are randomly selected, complete parts 1 and 2

GROUP

O A B AB

Type RH+ 83 56 17 15

RH- 19 15 4 2

1) Assume that the selections are made with replacements. What is the probability that the 2 selected subjects are both group A and type Rh+? _____ (round to four decimal places)

2) Assume the selections are made without replacements. What is the probability that the 2 selected subjects are both group A and type Rh+? _____ (round to four decimal places)

A research center poll showed 80% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is ____ (integer or decimal)

See file.

thanks

An urn contains five white and four black balls. Four balls are transferred to a second urn…

There are 20 people in a room, 15 men and 5 women. Ten of the men are 30 years of age or older and the other five are under 30. Four of the women are under 30 and one is over 30.

If I pick a person at random what is the probability of picking a man? A woman?

If I pick a person at random what is the probability the person will be male or over 30?

If I pick a person at random what is the probability the person will be female or under 30?

If I pick two people at random what is the probability of picking a man on the first pick and a woman on the second without replacement? What would the probability be with replacement?

Please see the attached problem.

The mean salary offered to students who are graduating from Coastal State University this year is 24275 , with a standard deviation 3712 of . A random sample of 75 Coastal State students graduating this year has been selected. What is the probability that the mean salary offer for these 75 students is 25000 or more?

I need help finding which kind of probability it is, and how to solve it.

2. The demand for a product of ABC company varies greatly from month to month. The probability distribution of the company’s monthly demand is given in the following table

Demand (in units) Probability

300 0.20

400 0.30

500 0.35

600 0.15

(a) If the company orders the expected monthly demand amount, what should ABC’s monthly order quantity be for this product?

(b) Assume that ABC company orders the amount in (a), what is the probability that the company has the stock-out problem? (Note: (i) stock-out problem means that the demand is greater than the on-hand stock for the month; (ii) we assume that the company can only order once at the beginning of the month.)

(c) Compute the standard deviation of the monthly demand?

(d) Assume that each unit sold generates $70 in revenue and that each unit ordered cost $50. If the monthly order quantity is chosen to be 500 units, what is the expected monthly profit? (note: Profit=Revenue – Cost)

1. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

a. 0.3551

b. 0.3085

c. 0.2674

d. 0.1915

2. The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.5 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3.4 and 3.7 pounds?

a. 0.5478

b. 0.2935

c. 0.8413

d. 0.1859

3. If n = 10 and p = 0.70, then the mean of the binomial distribution is:

a. 0.07

b. 1.45

c. 7.00

d. 14.29

The probability that Tracy Morris will due during the 10-year term of a life insurance policy is assessed by the insurance company at 1/5. Arthur Average’s probability of living to the end of the 10-year period is reckoned at 95% What is the probability that at the end of the 10 years (a) both (b) one of the other, but not both is living?

1. A group of volleyball players consists of four Grade-11 students and six Grade-12 students. If six players are chosen at random to start a match, what is the probability that three will be from each grade?

2. If a bowl contains ten hazelnuts and eight almonds, what is the probability that four nuts randomly selected from the bowl will all be hazelnuts?

3. If you simultaneously roll a standard dice and spin a spinner with eight equal sectors numbered 1 to 8. What is the probability of both rolling an even number and spinning an odd number?

4. A bag contains three green marbles and four black marbles. If you randomly pick two marbles from the bag at the same time, what is the probability that both marbles will be black?

5. What is the probability of rolling a total of 7 in two rolls of a standard dice if you get an even number on the first roll?

15. Industry standards suggest that 10 percent of new vehicles require warranty service

within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday.

a. What is the probability that none of these vehicles requires warranty service?

b. What is the probability exactly one of these vehicles requires warranty service?

c. Determine the probability that exactly two of these vehicles require warranty service.

d. Compute the mean and standard deviation of this probability distribution.

Data collected from town A shows that 60% of drivers are above 30 years old. 5% of all the drivers over 30 will be prosecuted for a driving offense during a year, compared with 10% of drivers aged 30 or younger. If a driver has been prosecuted, what is the probability they are 30 or younger?

10.The number of cars arriving at Joe Kelly’s oil change and tune-up place during the last 200 hours of operation is observed to be the following:

Number of cars arriving Frequency

3 or less 0

4 10

5 30

6 70

7 50

8 40

9 or more 0

Determine the probability distribution of car arrivals.

Answer the following questions based on the assumption that genotypes BB and Bb have brown eyes, while bb has blue eyes. Filled in the symbols in the pedigrees that represent blue eyes.

a) What is the probability that the first child of a mating between II-2 and II-7 would be a blue-eyed girl?

b) What is the probability that the first child of a mating between II-3 and II-8 would be blue-eyed?

c) What is the probability that II-6 is homozygous?

d) What is the probability that the first child of II-3 and II-8 would be a brown-eyed boy?

(see diagram in the attached file)

Researchers at the University of Nevada at Reno asked a sample of county commissioners to give their perception of the single most important factor in identifying study of urban countries (Professional Geographer, Feb. 2000.) In all, five factors were mentioned by the commissioners; total population, agricultural change, presence of industry, growth and population concentration.

The survey results are displayed in the following pie chart. (Values in the chart are percentages.) Forty-five percent of country commissioners in Nevada feel that “population concentration” is the single most important factor used in identifying urban counties. Suppose 10 county commissioners are selected at random to serve on a Nevada review board that will consider redefining urban and rural areas.

A. What is the probability that more than half of the commissioners will specify “population concentration” as the single most important factor used in identifying urban counties?

(See attached file.)

An on the job injury occurs once every 10 days on average, at an auto plant. WHat is the probability that the next on the job injury will occur within 10 days?

A. .9513

B. .8647

C. .6500

D. .6321

The probability that a standard normal random variable, Z, is between 1.00 and 3.00 is:

A. 0.1574

B. 0.3158

C. 0.5456

D. 0.9544

Use a tree diagram.

Use a diagram to list the sample space showing possible arrangements of heads and tails when four coins are tossed . Then use the sample space to find the probability that:

1. at most two coins come up heads

2. at least two coins come up heads

3. no more than three coins come up tails.

1 ) The following are measurements of the diameter of engine crankshafts in millimeters. The process mean is supposed to be 224. What is the probability that a similar study would have the same sample mean or higher?

224.120 224.001 224.017 223.989 223.960 223.961 224.089

2) Cola drink makers try to keep the sweetness of their drink consistent. In checking the sweetness of several samples, they found the following values present. The claimed sweetness measure for the drink is 4.0 Higher number represent more sweetness. What is the probability that this drink is sweeter than the claim?

4.8 3.75 4.6 4.1 4.0 4.25 4.45

3) An WIAS test for adults has had a mean of 105 and a standard deviation value of 13

a. What is the probability of a random chosen person having a score of 107 or lower?

b. What is the probability of 60 random chosen person having a score of 107 or lower?

4) Recent study of television viewing, 73% of first year college students stated that university well off financially is a very important personal goal. A state university found that 66% of their students agreed with this statement. If a group of 200 students is sampled what is the probability that the school percentage or higher will be found?

3. At a certain university, 30% of the students major in mathematics. Of the students majoring in mathematics, 60% are males. Of all the students at the university, 70% are males.

a. What is the probability that a student selected at random in the university is male and majors in mathematics?

b. What is the probability that a randomly selected student in the university is female or majors in mathematics or both?

Use of TI – 83 plus calculator is permitted given that steps are provided.

1. An MBA new-matriculates survey provided the following data for 2018 students.

Applied to more than one school

Yes No

23 and under 207 201

24 – 26 299 379

27 – 30 185 268

31 – 35 66 193

36 and over 51 169

a) Given that a person applied to more than one school, what is the probability that the person is 24 – 26 years old?

b) Given that a person is in the 36 and over age group, what is the probability that the person applied to more than one school?

c) What is the probability that a person is 24 – 26 years old or applied to more than one school?

d) Suppose a person is known to have applied to only one school. What is the probability that the person is 31 or more years old?

36. An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment.

39. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces:

a) Exactly 5 will be defective?

b) 5 or more will be defective?

32. A tube of Listerine Tartar Control toothpaste contains 4.2 ounces. As people use the toothpaste, the amount remaining in any tube is random. Assume the amount of toothpaste left in the tube follows a uniform distribution. …

[Please the attached questions file.]

Solve the following problems showing your work:

1. Suppose you have 4 nickels, 6 dimes, and 4 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that

a. You will draw a dime?

b. You will draw a nickel?

c. You will draw a quarter?

2. You are rolling a pair of dice, one red and one green. What is the probability of the following outcomes:

a. The sum of the two numbers you roll from the dice is 11.

b. The sum of the two numbers you roll is 6.

c. The sum of the two numbers you roll is 5.

3. A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble?

Suppose we have two stocks, stock A and stock B. Suppose that each stock has the following probabilities of decreasing (D), remaining unchanged (U) and rising (R), and that they are independent.

Stock A: P(D)=.2, P(U)=.1 and P(R)=.7

Stock B: P(D)=.3, P(U)=.3 and P(R)=.4

Let X=0,1,2 be the the number of stocks that RISE. Thus, x is a random variable. FIND THE CORRESPONDING PROBABILITIES P(0), p(1), and P(2). Verify that this turns out to be a probability distribution.

Refer to table 3B.

If a bill is chosen at random what is the probability that it is either for the Midwest or from the South?

Given the bill is from the east what is the probability that it is for a physicians visit? …

[See the attached questions file.]

This is a statistics question that I cannot get a handle on, so I would appreciate your help. Please show the work for future reference. Thank you very much.

A study of Hub Furniture regarding the payment of invoices reveals the time from billing until payment is received follows the normal distribution. The mean time until payment is received is 20 days and the standard deviation is 5 days.

a. What percent of the invoices are paid within 15 days of receipt?

b. What percent of the invoices are paid in more than 28 days?

c. What percent of the invoices are paid in more than 15 days but less than 28 days?

d. The management of Hub Furniture wants to encourage their customers to pay their monthly invoices as soon as possible. Therefore, it announced that a 2 percent reduction in price would be in effect for customers who pay within 7 working days of the receipt of the invoice. What percent of customers will earn this discount?

If you ask three strangers about their birthdays, what is the probability: (a) All were born on Wednesday? (b) All were born on different days of the week? (c) None were born on Saturday?

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. One classic use of the normal distribution is inspired by a letter to dear abby in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the US Navy. given this information, find the probability of a pregnancy lasting 308 days or longer.

Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic cards in making purchases. The results of the study provided the following probabilities.

-The probability that a consumer uses plastic card when making a purchase is .37.

-Given that the consumer uses a plastic card, there is a .19 probability that the consumer is 18-24 years old.

-Given that the consumer uses a plastic card, there is a .81 probability that the consumer is more than 24 years old.

U.S. Census Bureau data show that 14% of the consumer population is 18-24 years old.

A. Given the consumer is 18-24 years old, what is the probability that the consumer uses a plastic card?

B. Given the consumer is over 24 years old, what is the probability that the consumer uses a plastic card?

C. What is the interpretation of the probabilities shown in parts (a) and (b)?

D. Should companies such as Visa, MasterCard, and Discovery make plastic cards available to the 18-24 year-old age group before these consumers have had time to establish credit history? If no, why? If yes, what restrictions might the companies place on this age group?

The manager of a restaurant believes that waiters and waitresses who introduce themselves by telling customers their names will get larger tips than those who don’t. In fact, she claims that the average tip for the former group is 18%, whereas that of the later is 15%. If tips are normally distributed with a standard deviation of 3%, what is the probability that in a random sample of 10 tips recorded from waiters and waitresses who introduce themselves and 10 tips from those who don’t, the mean of the former will exceed that of the latter?

The red lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is the probability that less than 70% rate the food as excellent?

The restaurant in a large commercial building provides coffee for the building’s occupants. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new tenant of the building intends to have a total of 125 new employees. What is the probability that the new employees will consume more than 240 cups per day?

The heights of north American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

a) What is the probability that a randomly selected woman is taller than 66 inches?

b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?

c) What is the probability that the mean height of a random sample of 100 women is greater than 66 inches?

Assume the probability of the birth of a boy is 0.5. …

[See the attached question fle.]

A silver dollar is flipped twice, calculate the probability of each of the following occurring:

A, a head on the first flip

b, a tail on the second flip given that the first toss was head

c, two tails

d, tail on the first tail on the second

e, tail on the first a head oon the second or a head on the first tail on the second

f, at least one head n the two flips

A production process manufacturers alternators. On the average, 1% of the alternators will not perform properly when tested in the plant. When a large shipment of alternators is received at the plant, 100 are tested, and, if more that 2 are defective, the shipment is returned to the manufacturer. What is the probability of returning a shipment?

An ice chest contains six cans of apple juice, eight cans of grape juice, four cans of orange juice,and 2 cans of mango juice. Suppose that you reach into the container and selected 2 cans in succession. What is the probability of selecting a can of apple juice? A can of grape juice then a can of orange juice?

A coin is tossed and a die is rolled. Find the probability of getting a tails and a number greater than 2.

1 Flying approximately 40 billion passenger -miles per month , US airlines average a bout 4 fatalities per month . Assume that probability distribution for X , the number of fatalities per month , can be approximated by a Poisson probability distribution . What is the probability that more than two fatalities will occur in September 2007.

Twenty scientists are seeking financial support from the National Science Foundation . Find the number of ways in which the NSF panel can select four of the twenty submitted proposals ranking them as first , second , third , and fourth.

A state runs a lottery in which 6 numbers are randomly selected from 40, without replacement. A player chooses 6 numbers before the state’s sample is selected.

a. What is the probability that the 6 numbers chosen by the player match all 6 numbers in the state’s sample?

b. What is the probability that 5 of the 6 numbers chosen by the player match all 6 numbers in the state’s sample?

c. What is the probability that 4 of the 6 numbers chosen by the player match all 6 numbers in the state’s sample?

d. If the player enters one lottery each week, what is the expected number of weeks until a player matches all 6 numbers in the state’s sample?

See attached and solve for 1, 3, 5 and 9 only. Give step by step solution with every minor detail.

1. During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person.

2. If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 6?

A) 2 out of 3 B) 1 out of 3 C) 1 out of 6 D) 1 out of 2 E) 5 out of 6

3. A jar contains 5 yellow marbles, 16 green marbles, and 8 black marbles. If one marble is selected at random, what is the probability that it is not green?

4. One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is a red king.

5. The odds against Thunderbolt winning the Sarasota Derby are 9: 2. Find the probability that Thunderbolt wins.

A) 9/20 B) 11/20 C) 9/11 D) 2/11 E) 2/9

6. 1000 tickets for prizes are sold for $2 each. Seven prizes will be awarded – one for $400, one for $200, and five for $50. Steven purchases one of the tickets.

a) Find the expected value

b) Find the fair price of the ticket.

7. ( Two balls are to be selected without replacement from a bag containing one red, one blue, one green, one yellow, and one black ball. How many points are there in the sample space?

8. A license plate is to consist of two letters followed by three digits. How many different license plates are possible if the first letter must be a vowel, and repetition of letters is not permitted, but repetition of digits is permitted?

9. A man has 8 pairs of pants, 5 shirts, and 3 ties. How many different outfits can he wear?

10. A specific brand of bike comes in two frames, for males or females. Each frame comes in a choice of two colors, red and blue, and with a choice of three seats, soft, medium, and hard.

a) Use the counting principle to determine the number of different arrangements of bicycles that are possible.

b) Construct a tree diagram illustrating all the different arrangements of bicycles that are possible.

c) List the sample space.

11. The results of a survey for an airline are shown below

Traveler Male Female Total

Business 57 92 149

Vacation 72 74 146

Total 129 166 295

Use the chart to find the probability that the traveler was

a) male

b) on vacation given the traveler was male

c) female given the traveler was on business

12. In how many ways can 7 instructors be assigned to seven sections of a course in mathematics?

13. At an annual flower show, 6 different entries are to be arranged in a row.

a) How many different arrangements of the entries are possible?

b) If the owners of the 1st, 2nd, and 3rd place entries will be awarded prizes of $100, $50, and $25 respectively, how many ways can the prizes be awarded?

14. How many different ways are there for an admissions officer to select a group of 7 college candidates from a group of 19 applicants for an interview?

Consider four cards on each of which is marked off side 1 and side 2 …

[Please see the question file for full description of the problem.]

Complete the practice question in an excel spreadsheet and display the profit for each model in a bar chart.

After 12 months in business, you discover that only 10 percent of people who walk through your doors will be buyers. Of those who buy vehicles, the breakdown of vehicle purchases is as follows:

VW Golf 15%

Saab 92X 15%

BMW Z4 20%

Skoda Octavia 10%

Lada Niva 40%

1. What is the probability that a potential customer will buy a BMW Z4? A Skoda?

2. If in June, 200 people walk through the doors of your dealership, how many will buy a Lada Niva?

After all selling expenses are removed, you make the following profits from the sale of each vehicle type:

VW Golf $1,000

Saab 92X $2,000

BMW Z4 $12,000

Skoda Octavia $1,200

Lada Niva $400

3. What is the probability that a customer will walk through the door and provide you with at least a $1,000 profit?

4. If 400 people walk through the door in a month, what is your total expected profit?

5. Based on the figures, should you continue selling your favorite car, the Lada Niva? Why or why not?

A) In a (poorly run) widget factory, it is known that 25% of all products off the line will be defective. A random sample of 5 widgets is taken on a certain day. What is the probability that all of the widgets are defective? What is the probability that none are defective?

B) A coin is flipped 5 times in a row. What is the probability that it will come up tails all five times? What is the probability that it will come up tails exactly 4 times?

Managerial decision making

Chapter 5#18

Let P(X) =.55 and P(Y) =.35

Assume the probability that they both occur is .20

What is the probability of either X or Y occurring?

[See the attached question file.]

A computer specialty manufacturer has a two-person technical support staff who work independently of each other. In the past, Tom has been able to solve 75% of the problems he has handled, and Adam has been able to solve 95% of the problems he has handled. Incoming problemsm are randomly assigned to either Tom or Adam.

If a technical problem has just been assigned to the support department, what is the probability that it will be handled by Adam?

If it turns out that the problem was solved, what is the probability that it was handled by Adam?

Fire Fatalities

If computations are used, please use an Excel worksheet to show them or state response in a form that can be transferred to a spreadsheet.

Using the table below, how many victims were in the category

described by:

a. (A and A′)?

b. (C or F)?

c. (A′ and G′)?

d. (B or G′)?

Table

The following contingency table of frequencies is based on a 5-year

study of fire fatalities in Maryland. For purposes of clarity, columns

and rows are identified by letters A-C and D-G, respectively.

SOURCE: National Fire Protection Association, The 1984 Fire Almanac, p. 151.

Blood Alcohol

Level of Victim

A B C

0.00% 0.01-0.09% > 0.10%

D 0-19 142 7 6 155

E 20-39 47 8 41 96

F 40-59 29 8 77 114

G 60 or more 47 7 35 89

265 30 159 454

(5.13)

A survey of top executives revealed that 35 percent of them regularly read Time magazine, 20 percent read Newsweek, and 40 percent read U.S. News and World Report. Ten percent read both Time and U.S. News and World Report.

a. What is the probability that a particular top executive reads either Time or U.S. News and World Report regularly?

b. What is the probability .10 called?

c. Are the events mutually exclusive? Explain

A bag contains 8 black balls and 6 white balls. Two balls are drawn out at random, one after the other without replacement. calculate the probabilities that

(a) The second ball is black

(b) The first ball was white, given that the second ball is black.

Suzy and Fran toss a coin over cab fare. The probability that Suzy will pay five days in a row is 0.03125.

True or False?

Please write the probability formula for each one.

1. Twenty five scientists are seeking financial support from the National Science Foundation. Find the number of ways in which the NSF panel can select four of the twenty five submitted proposals ranking them as first second , third , and fourth.

2. A basket contains 6 red apples and 9 green apples . A sample of 5 apples is drawn. Find the probability that the sample contains

a. Five red apples?

b. Two red and three green apples?

c. at lest one red apple?

3. If two cards are drawn fro0mthe standard deck without replacement, find the probability that :

a. The first card is red, and the second is black

b. Both cards are aces

4. There are seven cards with digits 0,1, 2, 3, 4, 5, and 6. A child takes four of the cards and places them in some order. What is the probability that he obtains a four-digit number less than 3265?

Please include the formula for each part of these question and show all steps. Thank you

1. Roughly speaking, what is an experiment? An event? Give an example of each. …

[See the attached Question File.]

Note that answers are given. Please show the workings to arrive at the answers.

An auditor for an insurance company in Alberta reports 40 percent of the policyholders 55 years or older submit a claim during the year. 15 policyholders are randomly selected for company records

a) how many of the policyholders would you expect to have a filed a claim within the last year? Ans; 6

b) What is the probability that 10 of the selected policyholders submitted a claim last year? Ans: 0.0245

c) What is the probability that 10 or more of the selected policyholders submitted a claim last year? Ans: 0.0338

d) What is the probability that less than six of the selected policyholders submitted a claim last year? Ans: 0.4032

Suppose a certain test detects cancer among people …

[See the attached question File.]

Jim’s systolic blood pressure is a random variable with a mean of 145 mmHg and a standard deviation of 20 mmHg. For Jim’s age group, 140 is the cutoff for high blood pressure.

If Jim’s systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be, (a) 135 or less?

(b) 175 or more?

(c) between 125 and 165?

If a= 0.05, what is the probability of making a Type I error?

a.0

b.1/20

c. 19/20

d. 20/20

Using Excel, please demonstrate use of functions to solve the following probability problem.

Tired of careless spelling and grammar, a company decides to administer a test to all job applicants. The test consists of 20 sentences. Applicants must state whether each sentence contains any grammar or spelling errors. Half the sentences contain errors. The company requires a score of 14 or more.

If an applicant guesses randomly, what is the probability of passing? (Round your answer to 4 decimal places.)

What minimum score would be required to reduce the probability “passing by guessing” to 5 percent or less?

Dotties Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 15 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 63 returns. What is the probability that she makes errors on:

(a) More than 6 returns?

(b) At least 6 returns?

(c) Exactly 6 returns?

Ans:

a) 0.0192

b) 0.0694

c) 0.0502

Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans.

a. What is the probability that 3 loans will be defaulted?

b. What is the probability that at least 3 loans will be defaulted?

Ans; 0.0613

0.0803

Problem 1. A local bank reports that 80 percent of its customers maintain a checking account, 60 percent have a savings account, and 50 percent have both.

If a customer is chosen at random, what is the probability the customer has either a checking or a savings account?

What is the probability the customer does not have either a checking or a savings account?

Problem 2. A recent study of the hourly wages of maintenance crew members for major airlines showed that the mean hourly salary was $20.50, with a standard deviation of $3.50. If we select a crew member at random, what is the probability the crew member earns: a. Between $20.50 and $24.00 per hour? b. More than $24.00 per hour? c. Less than $19.00 per hour?

a. What is the probability the crew member earns: a. Between $20.50 and $24.00 per hour?

b. What is the probability the crew member earns more than $24.00 per hour?

c. What is the probability the crew member earns less than $19.00 per hour?

Residents of Mill River have fond memories of ice skating at a local park. An artist has captured the experience in a drawing and is hoping to reproduce it and sell framed copies to current and former residents. He thinks that if the market is good he can sell 400 copies of the elegant version at $1.25 each. If the market is not good, he will sell only 300 at $90 each. He can make a deluxe version of the same drawing instead. He feels that if the market is good he can sell 500 copies of the deluxe version at $100 each. If the market is not good, he will sell only 400 copies at $70 each. In either case, production costs will be approximately $35,000. He can also choose to do nothing at this time. If he believes there is a 50% probability of a good market, what should he do? Why?

During a 36 year period, lightening killed 2768 people in the US. Assume that this rate holds true today and is constant throughout the year. Find the probability that tomorrow

a) no one in the US will be struck and killed by lightening

b) one person will be struck and killed

c) more than one person will be struck and killed

62. Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random sample of 200 antennas, find the probability that:

a. None of the antennas is defective.

b. Three or more of the antennas are defective.

Please help with the following problems.

Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm’s public relations office. Their employer must choose two of them to attend a conference in Paris.

To be fair, the choice will be made by drawing two names from a hat. (This is an SRS of size 2)

a) Write down all the possible choices of two of the five names. This is the sample space.

b) The random drawing makes all the choices equally likely. What is the probability of each choice?

c) What is the probability that Mei-Ling is chosen?

d) What is the probability that neither of the two men (Sam and Roberto) is chosen?

The Connecticut State Highway Patrol claims that the average speed of the 2000 cars driving Interstate 91 from Hartford to New Haven on June 20 between 10:00AM and 11:00AM is 71 mph with a standard deviation of 5 mph. By coincidence the Connecticut Safety Council sampled 50 cars on Interstate 91 from Hartford to New Haven on June 20 between 10:00AM and 11:00AM and found the average speed was 73 mph. What is probability of finding a sample mean of 73 mph or more?

Please use the attachments provided and not only excel functions.

Please see attached files for question. I can’t seem to get the answer for PART3.

(See attached file for full problem description with equations)

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A bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up window occur at random, with a mean arrival rate of 24 customers per hour or 0.4 customers per minute.

1) What is the mean or expected number of customers that will arrive in a five minute period?

Denote by the number of customers in the i-th minute. So, . Hence,

2) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the mean arrival rate in part 1 and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period.

By part 1), we know that the mean or expected number of customers that will arrive in a five minute period is 2. So, . Denote by X the number of customers will arrive during a five-minute period.

3) Delays are expected if more than three customers arrive during any five-minute period. What is the probability thsat delays will occur?

P(X>3)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)

=1-

So, the probability thsat delays will occur is 0.145

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18. According to an IRS study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. A consumer watchdog agency selects a random sample of 40 taxpayers and finds the standard deviation of the time to prepare, copy, and electronically file form 1040 is 80 minutes.

a. What assumption or assumptions do you need to make about the shape of the population?

b. What is the standard error of the mean in this example?

c. What is the likelihood the sample mean is greater than 320 minutes?

d. What is the likelihood the sample mean is between 320 and 350 minutes?

e. What is the likelihood the sample mean is greater than 350 minutes?

Modern aircraft engines are very reliable. One feature contributing to that reliability is the use of redundancy, where critical components are duplicated so that if one fails, the other will work. For example, single-engine aircraft now have two independent electrical systems so that if one electrical system fails, the other can continue to work so that the engine does not fail. We will assume that the probability of electrical system failure is 0.001.

a. If the engine and aircraft has one electrical system, what is the probability that it will work?

b. If the engine and aircraft has two independent electrical systems, what is the probability that the engine can function with a working electrical system?

c. What rule of probability does this problem represent?

The single shot probability of kill of any weapon system (gun, missle or slingshot) is less than 1 due to the reliability factors if no other reason. Suppose the single shot probability of kill of a new defensive missle system is 0.75%, and the the probability is not considered adequate. One familiar strategy to increase the overall probability of a defensive kill is to launch several defensive missiles at one incoming threat.

Let Pk (P underscore k) stand for the single shot probability of kill and Pt (P underscore t) stand for the overall probability of kill.

a) Develope a formula for the overall probability of kill, assuming that N defensive missles are launched.

b) You will have had to make a probabilistic assumption in order to develope the formula. What was that assumption?

1. A particular spell has a .18 (i.e. 18%) chance to do critical damage. What is the probability that a spell can be cast 10 times in a row without doing critical damage?

A) .137 B) .820 C) .862 D) <.001

2. What is the probability of the sum of two dice equaling an odd number?

A) .50 B) .38 C) .25 D) .61

3. A coin is tossed 10 times. What is the probability that the coin will come up heads exactly 4 times?

A) .50 B).21 C) .40 D) .24

4. What is the probability of rolling 3 or higher on a die roll, if the roller has the option to re- – roll the die a single time?

A) .66 B) .50 C) .75 D) .89

A numerical answer to each question must be given. Please show all work

5. A treasure chest contains 5 rubies, 8 diamonds, 7 emeralds, and 4 sapphires. If you pick a gem at random, what is the probability of choosing a ruby?

6. A squad based combat game is designed to consider kills and objectives equally and award top players a special honor. Analysis of games indicated a 63% chance that the top player has the most kills, a 50% chance of achieving the most objectives, and a 35% chance of having the most kills AND achieving the most objectives. What is the probability of a player earning the special honor for only getting the most kills OR only achieving the most objectives?

7. In a particular fighting game, a boxing character is given 7 to 5 odds against a karate character.

What is the probability of the boxer winning?

8. You roll a die and it comes up 6. If you roll a second die and add up the values of the two dice,

what is the probability that the sum will be 8 or higher?

9. A coin has been flipped 6 times, coming up heads each time. What is the probability that the

coin will come up tails on the 7th flip?

10. A video game publisher noted that 80% of their titles came from Studio 1 and 20% came from their Studio 2. 85% percent of the titles from Studio I make a profit, while only 70% of the titles from

Studio 2 are profitable. What is the probability that a title will come from Studio 2 and be profitable?

11. In a game you are required to roll 3 dice and choose the lowest 2 results (i.e. discard the highest result). What is the probability that the sum of the dice is 7 or greater?

1. A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

2. How many riders would there have to be on a bus to yield (a) a 50 percent probability that at least two will have the same birthday? (b) A 75 percent probability?

1. A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 20%. She also believes that if the economy enters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession the probability that the mutual fund will increase in value is 75%. Find the probability that the mutual fund’s value will increase.

2. Three airlines serve a small town in the country. Air A has 50% of all the scheduled flights, Air B has 30%, and Air C has the remaining flights. Their on-time rates are 40%, 65%, and 80%, respectively. A plane has just left on time. What is the probability that it was Air A?

Let X be a normally distributed random variable with µ = 100 and σ = 10. The probability that X is between 70 and 110 is (to the nearest whole percent)

a. 8 %

b. 84 %

c. 95%

d. answer not listed

In a survey on the quality of customer service at Car Toys, customers were asked to rate the service on a scale from 1 to 10, with 10 being that a customer was completely satisfied. Assume that the distribution of the responses can be approximated by a normal distribution with a mean of 7 and a std deviation of 1.

a. What is the probability that an individual customer gives a rate of at least 8?

b. In a random sample of 10, what is the probability that the average rating is at least 8?

(Please explain each step with any formulas)

Suppose that you select 2 cards without replacement from an ordinary deck of playing cards.

a. If the first card that you select is a king, what is the probability that the second card that you select is a heart?

b. If the first card that you select is a heart, what is the probability that the second card that you select is a club?

c. If the first card that you select is a diamond, what is the probability that the second card that you select is the jack of diamonds?

If three parts are selected at random from the bin, what is the probability that exactly two are defective? Please explain step by step.

In class we are learning about conditional probability and independence.

The question is: On a multiple-choice test you know the answers to 70% of the question (and get them right), and for the remaining 30% you choose randomly among the 5 answers. What percent of the answers should you expect to get right?

At a university with 1000 business majors, 20% are enrolled in a statistics course. Of these 200 students enrolled in the statistics course, 25% are also enrolled in an accounting course. There are 250 students who are enrolled in accounting and not enrolled in statistics. Of the students is enrolled in statistics, what is the probability that the student is not enrolled in accounting?

Given the following table of payoffs use sensitivity analysis to determine at what probability or more you would select decision 3.

s1 s2

d1 8 10

d2 2 15

d3 10 3

a none of the choices are correct

b .5798

c .5454

d.4545

e .7778

Employees of a company fall into four categories: Managers (4%),

Administrators (12%), Technicians (26%) and Labourers (58%).

If 20% of the Managers, 5% of the Administrators, 3% of the Technicians

and 0.5% of the Labourers have the opportunity of promotion in the next

year:

(i) What is the probability that a randomly chosen employee is a

manager and will gain promotion next year?

(ii) What is the probability that a randomly chosen employee will gain

promotion next year?

(iii) What is the probability that a randomly chosen employee is an

Administrator if the employee has the opportunity of gaining

promotion next year?

There are two urn, a green urn and a red urn.

The green urn contains 17 green balls and the red urn contains 15 red balls.Each round, one ball is chosen randomly from either urn.

The probability that the green urn on any given round is chosen is 4/7.

The probability that the red urn is chosen is 3/7.

What is the probability that there are exactly 6 red balls remaining at the moment the green urn is discovered to be empty?

1. According to the empirical rule, if the data form a “bell-shaped” normal distribution, ________ percent of the observation will be contained within 1 (one) standard deviation around the arithmetic mean.

68.26

75.00

88.89

93.75

2. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new add campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are independent, the probability that the cost is kept withing budget and the campaign will increase sales is:

0.20

0.32

0.40

0.88

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

a. 1/4

b. 1/8

c. 5/8

d. 2/5

Past records have shown that the average number of accidents in a certain factory per person per year was 0.3. What is the probability that a randomly selected employee will have at least one accident during the coming year?

a) 0.259

b) 0.300

c) 0.741

Suppose that a telemarketer calls a random sample of 12 households in a community in the night that 80% of the households have someone at home. Find the probability that the person doing the calling finds someone at home in exactly 10 households.

a) 10.0%

b) 28.3%

c) 80.0%

Find the mean of the above distribution.

a) 8.0 households

b) 9.6 households

c) 10.0 households

Please see the attached file.

I Would Like Problems Resolved In EXECL IN EXCEL VERSION (No Higher Than version 2003)

Question #1

A gambler in Las Vegas is cutting a deck of cards for $1,000. What is the probability that the cards for the gambler will be the follow?

1. A face card

2. A queen

3. A Spade

4. A jack of spades

——————————————————

Question #2

The life of an electronic transistor is normally distributed, with a mean of 500 hour’ deviation of 80 hours. Determine the probability that a transistor will last for more than 400 hours.

—————————————————————-

Question #3

The Polo Development Firm is building a shopping center. 1t has informed renters that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping center is completed is estimated to be 14 months, with a standard deviation of 4 months, what is the probability that the renters will not be able to occupy in 19 months?

——————————————————————–

Question #4

A manufacturing company has 10 machines in continuous operation during a workday. The probability that an individual machine will break down during the day is .10. Determine the probability that during any given day 3 machines will break down.

—————————————————————————————————–

Questions # 5The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.

Questions #6 (IN EXCEL VERSION (no higher than 2003)

A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions:

Weather Conditions

Decision Rain Overcast Sunshine .?.

. 30 .15 .55

Sun visors $-500 $-200 $1,500

Umbrellas 2,000 0 -900

1. Compute the expected value for each decision and select the best one. 2. Develop the opportunity loss table and compute the expected opportunity loss for each decision.

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
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Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

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