CHAPTER 5: DISCRETE PROBABILITY DISTRIBUTIONS

1 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 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, mean 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) b) c) d) ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution 3. A PROBABILITY distribution is an equation that a) associates a particular PROBABILITY of occurrence with each outcome.

2 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. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: PROBABILITY distribution 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. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: expected value Copyright 2015 Pearson Education. 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.

3 C) Each outcome may be classified as either "event of interest" or "not event of interest.". d) The variable of interest is continuous. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 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. ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 7. Whenever = , the binomial distribution will a) always be symmetric. b) be symmetric only if n is large. c) be right-skewed. d) be left-skewed. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 8. Whenever = and n is small, the binomial distribution will be a) symmetric. b) right-skewed. c) left-skewed. d) None of the above. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties Copyright 2015 Pearson Education DISCRETE PROBABILITY DISTRIBUTIONS 5-3.

4 9. If n = 10 and = , then the mean of the binomial distribution is a) b) c) d) ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, mean 10. If n = 10 and = , then the standard deviation of the binomial distribution is a) b) c) d) ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, standard deviation 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. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Poisson distribution, mean, standard deviation, properties 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.

5 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. ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution, properties Copyright 2015 Pearson Education. 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. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: covariance, properties 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.

6 Corporate reports indicate that the PROBABILITY any one of their new cars needs a warranty repair in the first 90 days is 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. ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution, properties 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 The manager is interested in analyzing the PROBABILITY that any particular bag being inspected has fewer than blue chocolate chips.

7 A) binomial distribution. b) Poisson distribution. c) hypergeometric distribution. d) none of the above. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties Copyright 2015 Pearson Education 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. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution, properties 17. A stock analyst was provided with a list of 25 stocks.

8 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. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution, properties 18. A professor receives, on average, 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. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties Copyright 2015 Pearson Education.

9 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 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. ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 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. ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: portfolio, mean 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.

10 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. ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: hypergeometric distribution, properties Copyright 2015 Pearson Education DISCRETE PROBABILITY DISTRIBUTIONS 5-7. 22. On the average, 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. ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 23. A multiple-choice test has 30 questions.