effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject)
of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is
Suppose the test is given to
randomly selected people who do not have the antibody.
people?
people?
Here is a table showing all
cards in a standard deck.
Face cards  

Color  Suit  Ace  Two  Three  Four  Five  Six  Seven  Eight  Nine  Ten  Jack  Queen  King 
Red  Hearts 
A
♥ 
2
♥ 
3
♥ 
4
♥ 
5
♥ 
6
♥ 
7
♥ 
8
♥ 
9
♥ 
10
♥ 
J
♥ 
Q
♥ 
K
♥ 
Red  Diamonds 
A
♦ 
2
♦ 
3
♦ 
4
♦ 
5
♦ 
6
♦ 
7
♦ 
8
♦ 
9
♦ 
10
♦ 
J
♦ 
Q
♦ 
K
♦ 
Black  Spades 
A
♠ 
2
♠ 
3
♠ 
4
♠ 
5
♠ 
6
♠ 
7
♠ 
8
♠ 
9
♠ 
10
♠ 
J
♠ 
Q
♠ 
K
♠ 
Black  Clubs 
A
♣ 
2
♣ 
3
♣ 
4
♣ 
5
♣ 
6
♣ 
7
♣ 
8
♣ 
9
♣ 
10
♣ 
J
♣ 
Q
♣ 
K
♣ 
Suppose one card is drawn at random from a standard deck.
Answer each part. Write your answers as fractions in simplest form.


Two airplanes are flying in the same direction in adjacent parallel corridors. At time t = 0, the first airplane is 10 km ahead of the second one. Suppose the speed of the first plane (km/hr) is normally distributed with mean 545 and standard deviation 9 and the second plane’s speed is also normally distributed with mean and standard deviation 525 and 9, respectively.
(b) Determine the probability that the planes are separated by at most 10 km after 2 hr. (Round your answer to four decimal places.)
Despite all the safety instructions they have received, many drivers do not activate their turn signals before changing lanes on the highway  
leading to accidents and even fatalities. Historical data shows that about  30%  of drivers fail to signal before changing lanes  
A traffic safety officer observed  110  cars changing lanes on I66 over the course of his shift.  
(a)  What is the probability that more than  30  drivers will fail to activate their turn signal before changing lanes  
(b)  What is the standard deviation of the number drivers who do not activate their turn signals before changing lanes?  
(c)  What is the probability that between  18  and  26  drivers (both numbers included in the interval) will fail to use their turn signals  
before changing lanes? 
A service station has a pump that distributes diesel fuel to
automobiles. The station manager estimates that only 3.2 cars use
the diesel pump every 2 hours. Assume the arrivals of diesel pump
users are Poisson distributed.
(A) What is the probability that three to six cars will arrive to use
diesel pump during twohours period? Also find the expected
number of diesel pump users.
(B) What is the probability that at the most three cars will arrive to
use diesel pump during one hour period?
(C)Suppose the pump manager needs to shut down the diesel
pump for half an hour to make repairs. However, the owner
hates to lose any business. What is the probability of the
manager not losing the business during half an hour period?
(D)What is the probability that 3 or more cars will arrive to use
diesel pump during 45 minutes period?
A survey conducted by a food company in Flanders indicated that 13% of strawberry buyers could identify one or more strawberry brands. The survey also indicated that, out of the many strawberry providers, the best known brand is the one supplied by the above food company.
(a) What is the probability that at least 4 customers out of any 10 surveyed were able to identify any strawberry brand.
(b) Calculate the expected value, the variance, the standard deviation and the coefficient of variation of this distribution
Suppose there are two sixsided dice such that the probability on any roll of the first dice
resulting in a 4 is 0.2 and the probability on any roll of the second dice resulting in a 4 is 0.4.One of these dice are selected and is continually rolled until a 4 appears (at which point the
experiment stops). Assume there is a 0.3 probability the first dice is selected and that the rolls
of the dice are independent of each other.
(a) What is the probability that it will take four or more rolls of the dice until we
get our first 4? Please compute your answer to four decimal places.
(b) Suppose that it takes 5 rolls to obtain your first 4. What is the probability
that the first dice was selected? Please compute your answer to four decimal places.
The 70year longterm record for weather shows that for New York State, the annual precipitation has a mean of 39.84 inches and a standard deviation of 4.34 inches. The annual precipitation amount has a normal distribution. (Give your answers correct to four decimal places.)
(b) What is the probability that next year the total precipitation for New York State is between 41.7 and 47.4 inches?
(c) What is the probability that next year the total precipitation for New York State is between 30.7 and 38 inches?
and
suppose that
and
and
and
(Select all that apply.)
Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 92 and estimated standard deviation σ = 50. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
What is the probability that x < 40? (Round your answer to four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?
Explain what this might imply if you were a doctor or a nurse.
A recent study of how Americans spend their leisure time surveyed workers employed more than 5 years. They determined the probability an employee has 2 weeks of vacation time to be 0.45, 1 week of vacation time to be 0.10, and 3 or more weeks to be 0.20. Suppose 20 workers are selected at random.
(a) What is the probability that 8 have 2 weeks of vacation time?
(b) What is the probability that only one worker has 1 week of vacation time?
(c) What is the probability that at most 2 of the workers have 3 or more weeks of vacation time?
(d) What is the probability that at least 2 workers have 1 week of vacation time?
if
(Round your answers to three decimal places.)
When
When
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