Discrete Probability Distributions 5-1

CHAPTER 5: DISCRETE PROBABILITY DISTRIBUTIONS

1. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-

Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that

the teacher on bus duty will likely be certified in CPR?

a) 5 days

b) 45 days

c) 65 days

d) 81 days

2. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4

students is selected from the program to be interviewed about the introduction of a new fast food

outlet on the ground floor of the campus building, what is the probability that all 4 students

selected are undergraduate students?

a) 0.0256

b) 0.0625

c) 0.16

d) 1.00

3. A probability distribution is an equation that

a) associates a particular probability of occurrence with each outcome.

b) measures outcomes and assigns values of X to the simple events.

c) assigns a value to the variability of the set of events.

d) assigns a value to the center of the set of events.

4. The connotation "expected value" or "expected gain" from playing roulette at a casino means

a) the amount you expect to "gain" on a single play.

b) the amount you expect to "gain" in the long run over many plays.

c) the amount you need to "break even" over many plays.

d) the amount you should expect to gain if you are lucky.

5-2 Discrete Probability Distributions

5. Which of the following about the binomial distribution is not a true statement?

a) The probability of the event of interest must be constant from trial to trial.

b) Each outcome is independent of the other.

c) Each outcome may be classified as either "event of interest" or "not event of interest."

d) The variable of interest is continuous.

6. In a binomial distribution

a) the variable X is continuous.

b) the probability of event of interest

is stable from trial to trial.

c) the number of trials n must be at least 30.

d) the results of one trial are dependent on the results of the other trials.

7. Whenever

= 0.5, the binomial distribution will

a) always be symmetric.

b) be symmetric only if n is large.

c) be right-skewed.

d) be left-skewed.

8. Whenever

= 0.1 and n is small, the binomial distribution will be

a) symmetric.

b) right-skewed.

c) left-skewed.

d) None of the above.

Discrete Probability Distributions 5-3

9. If n = 10 and

= 0.70, then the mean of the binomial distribution is

a) 0.07

b) 1.45.

c) 7.00

d) 14.29

10. If n = 10 and

= 0.70, then the standard deviation of the binomial distribution is

a) 0.07

b) 1.45

c) 7.00

d) 14.29

11. If the outcomes of a variable follow a Poisson distribution, then their

a) mean equals the standard deviation.

b) median equals the standard deviation.

c) mean equals the variance.

d) median equals the variance.

12. What type of probability distribution will the consulting firm most likely employ to analyze the

insurance claims in the following problem?

An insurance company has called a consulting firm to determine if the company has an

unusually high number of false insurance claims. It is known that the industry proportion for

false claims is 3%. The consulting firm has decided to randomly and independently sample

100 of the company’s insurance claims. They believe the number of these 100 that are false

will yield the information the company desires.

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

5-4 Discrete Probability Distributions

13. The covariance

a) must be between -1 and +1.

b) must be positive.

c) can be positive or negative.

d) must be less than +1.

14. What type of probability distribution will most likely be used to analyze warranty repair needs on

new cars in the following problem?

The service manager for a new automobile dealership reviewed dealership records of the past

20 sales of new cars to determine the number of warranty repairs he will be called on to

perform in the next 90 days. Corporate reports indicate that the probability any one of their

new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls

for warranty repair are independent of one another and is interested in predicting the number

of warranty repairs he will be called on to perform in the next 90 days for this batch of 20

new cars sold.

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

15. What type of probability distribution will most likely be used to analyze the number of blue

chocolate chips per bag in the following problem?

The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.

When the production process is in control, the mean number of blue chocolate chips per bag

is 6.0. The manager is interested in analyzing the probability that any particular bag being

inspected has fewer than 5.0 blue chocolate chips.

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

Discrete Probability Distributions 5-5

16. What type of probability distribution will most likely be used to analyze the number of cars with

defective radios in the following problem?

From an inventory of 48 new cars being shipped to local dealerships, corporate reports

indicate that 12 have defective radios installed. The sales manager of one dealership wants to

predict the probability out of the 8 new cars it just received that, when each is tested, no

more than 2 of the cars have defective radios.

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

17. A stock analyst was provided with a list of 25 stocks. He was expected to pick 3 stocks from the

list whose prices are expected to rise by more than 20% after 30 days. In reality, the prices of

only 5 stocks would rise by more than 20% after 30 days. If he randomly selected 3 stocks from

the list, he would use what type of probability distribution to compute the probability that all of

the chosen stocks would appreciate more than 20% after 30 days?

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

18. A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.

To compute the probability of receiving at least 10 e-mails on such a day, he will use what type

of probability distribution?

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

5-6 Discrete Probability Distributions

19. A company has 125 personal computers. The probability that any one of them will require repair

on a given day is 0.025. To find the probability that exactly 20 of the computers will require

repair on a given day, one will use what type of probability distribution?

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

20. The portfolio expected return of two investments

a) will be higher when the covariance is zero.

b) will be higher when the covariance is negative.

c) will be higher when the covariance is positive.

d) does not depend on the covariance.

21. A financial analyst is presented with information on the past records of 60 start-up companies

and told that in fact only 3 of them have managed to become highly successful. He selected 3

companies from this group as the candidates for success. To analyze his ability to spot the

companies that will eventually become highly successful, he will use what type of probability

distribution?

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

Discrete Probability Distributions 5-7

22. On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery

store. What type of probability distribution can be used to find out the probability that there will

be no customer arriving at a checkout counter?

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

23. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who

has not studied for the test decides to answer all questions randomly. What type of probability

distribution can be used to figure out his chance of getting at least 20 questions right?

a) binomial distribution.

b) Poisson distribution.

c) hypergeometric distribution.

d) none of the above.

24. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab

conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per

week. Interpret this value.

a) Most of the weeks resulted in rat costs of $13.00.

b) The median cost for the distribution of rat costs is $13.00.

c) The expected or mean cost for all weekly rat purchases is $13.00.

d) The rat cost that occurs more often than any other is $13.00.

5-8 Discrete Probability Distributions

25.