A company operating in Bangladesh can be in one of the three legal states: enlisted,
going through the enlistment process, and not enlisted. You have data on 160 companies among which 112 were enlisted, 30 were going through the enlistment process, and 18 were not enlisted. If six companies are selected at random,
a. what is the probability that there will be two companies in each of the three categories?
b. Do you think correlation and regression are same? Explain very briefly.
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 41 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 5,000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will may be rejected?
the company will accept what %?
The company will reject what %?
In a recent year, the Better Business Bureau settled 75% of complaints they received. (Source: USA Today, March 2, 2009) You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Assume the population proportion of complaints settled for the computer stores is the 0.75, as mentioned above. Suppose your sample size is 162. What is the probability that the sample proportion will be at least 2 percent more than the population proportion?
Note: You should carefully round any z-values you calculate to at least 4 decimal places to match wamap’s approach and calculations.
Answer = (Enter your answer as a number accurate to 4 decimal places.)
Suppose the daily electricity use values at a manufacturing plant have an unknown distribution with mean 430kWh and standard deviation 24kWh. A sample of size n=120 is randomly taken from the population and the sum is taken. What is the probability that the resulting sum is between 51,700kWh and 51,800kWh?
z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
---|---|---|---|---|---|---|---|---|---|---|
0.0 | 0.5000 | 0.5040 | 0.5080 | 0.5120 | 0.5160 | 0.5199 | 0.5239 | 0.5279 | 0.5319 | 0.5359 |
0.1 | 0.5398 | 0.5438 | 0.5478 | 0.5517 | 0.5557 | 0.5596 | 0.5636 | 0.5675 | 0.5714 | 0.5753 |
0.2 | 0.5793 | 0.5832 | 0.5871 | 0.5910 | 0.5948 | 0.5987 | 0.6026 | 0.6064 | 0.6103 | 0.6141 |
0.3 | 0.6179 | 0.6217 | 0.6255 | 0.6293 | 0.6331 | 0.6368 | 0.6406 | 0.6443 | 0.6480 | 0.6517 |
0.4 | 0.6554 | 0.6591 | 0.6628 | 0.6664 | 0.6700 | 0.6736 | 0.6772 | 0.6808 | 0.6844 | 0.6879 |
0.5 | 0.6915 | 0.6950 | 0.6985 | 0.7019 | 0.7054 | 0.7088 | 0.7123 | 0.7157 | 0.7190 | 0.7224 |
0.6 | 0.7257 | 0.7291 | 0.7324 | 0.7357 | 0.7389 | 0.7422 | 0.7454 | 0.7486 | 0.7517 | 0.7549 |
0.7 | 0.7580 | 0.7611 | 0.7642 | 0.7673 | 0.7704 | 0.7734 | 0.7764 | 0.7794 | 0.7823 | 0.7852 |
An experiment consists of tossing an unfair coin (51% chance of landing on heads) a specified number of times and recording the outcomes.
a.
What is the probability that the first head will occur on the second trial? (Use 4 decimal places.)
b.
Does this probability change if we toss the coin three times? What if we toss the coin four times?
The probability changes for both three and four tosses.
The probability changes if we toss the coin four times, but does not change if we toss the coin three times.
The probability does not change for either three or four tosses.
The probability changes if we toss the coin three times, but does not change if we toss the coin four times.
c.
What probability distribution model do we use to compute these probabilities?
normal
geometric
binomial
poisson
d.
What is the probability that the first head will occur on the fourth trial? after the fourth trial? (Use 4 decimal places.)
P(4) =
P(n > 4) =
ACTIVITY |
IMMEDIATE PREDECESSOR |
OPTIMISTIC TIME |
MOST LIKELY TIME |
PESSIMISTIC TIME |
A |
__________ |
2 |
3 |
4 |
B |
__________ |
5 |
6 |
7 |
C |
__________ |
5 |
6 |
7 |
D |
A |
3 |
4 |
5 |
E |
A |
2 |
3 |
4 |
F |
C |
3 |
4 |
5 |
G |
C |
9 |
11 |
16 |
H |
B, E, F |
5 |
6 |
7 |
I |
F, G, H |
7 |
11 |
15 |
J |
H, I, D |
2 |
3 |
4 |
K |
D |
3 |
4 |
5 |
L |
I, J, K |
7 |
11 |
15 |
1. Two cards are drawn at random from an ordinary deck of playing cards. The first is not replaced before the second is drawn. What is the probability that:
a. Both cards are aces?
b. At least one card is black?
2. Using the following sample: 28, 30, 24, 30, 32, 40, 22, 25, 26, 34
a. Find the mean.
b. Find the median.
c. Find the mode.
d. Find the standard deviation.
e. Find the z-score for 30. (Assuming a normal distribution)
f. Find the range.
According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches, with a standard deviation of 0.06 inches. What is the probability that the mean daily precipitation will be 0.095 inches or more for a random sample of 40 November days (taken over many years)?
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
The average height of flowering cherry trees in a nursery is 11 feet. The heights are normally distributed with a standard deviation of 1.6, What is the probability that a tree is less than 13 feet tall?
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of ppm and a standard deviation of ppm. The Environmental Protection Agency takes a random sample of of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is ppm or more. Find the probability that the disposal of such capacitors will be regulated.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
In humans, the ABO blood type is under the control of autosomal multiple alleles. Red-green color blindness is a recessive x-linked trait. If two parents who are both type A and have normal vision produce a son who is color-blind and type O, what is the probability that their next child will be a female who has normal vision and is type O?
An army tank 2.2m wide needs to travel 19m to cross a minefield. The enemy that laid the minefield is known to have a standard practice of randomly placing 129 mines per hectare (10 000 m2). What is the probability that the tank will set off a mine?
Employee drug testing is done in the following manner. An employee is chosen at random and a urine specimen is taken. The specimen is divided into three vials and each vial is sent to an independent lab. If each lab has a 0.97 probability of detecting illegal drugs when they are present, what is the probability that all three labs detect the drugs.
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