chap05-TIF-BSAFC5.doc

Discrete Probability Distributions 159CHAPTER 5: DISCRETE PROBABILITY DISTRIBUTIONS1. 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 daysb) 45 daysc) 65 daysd) 81 daysANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: binomial distribution, mean2. 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) 0.0256b) 0.0625c) 0.16d) 1.00ANSWER:bTYPE: MC DIFFICULTY: DifficultKEYWORDS: binomial distribution3. A probability distribution is an equation thata) associates a particular probability of occurrence with each outcome in the sample space.b) measures outcomes and assigns values of X to the simple events.c) assigns a value to the variability in the sample space.d) assigns a value to the center of the sample space.ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: probability distribution4. The connotation expected value or expected gain from playing roulette at a casino meansa) 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:bTYPE: MC DIFFICULTY: Easy KEYWORDS: expected value5. Which of the following about the binomial distribution is not a true statement?a) The probability of 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 random variable of interest is continuous.ANSWER:dTYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties6. In a binomial distributiona) the random 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:bTYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties7. Whenever p = 0.5, the binomial distribution willa) always be symmetric.b) be symmetric only if n is large.c) be right-skewed.d) be left-skewed.ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties8. Whenever p = 0.1 and n is small, the binomial distribution will bea) symmetric.b) right-skewed.c) left-skewed.d) None of the above.ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties9. If n = 10 and p = 0.70, then the mean of the binomial distribution is a) 0.07b) 1.45.c) 7.00d) 14.29ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, mean10. If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is a) 0.07b) 1.45c) 7.00d) 14.29ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, standard deviation11. If the outcomes of a random variable follow a Poisson distribution, then theira) mean equals the standard deviation.b) median equals the standard deviation.c) mean equals the variance.d) median equals the variance. ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: Poisson distribution, mean, standard deviation, properties12. 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 companys 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) normal distribution.d) none of the above.ANSWER:aTYPE: MC DIFFICULTY: DifficultKEYWORDS: binomial distribution, properties13. 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) normal distribution.d) none of the above.ANSWER:aTYPE: MC DIFFICULTY: DifficultKEYWORDS: binomial distribution, properties14. What type of probability distribution will most likely be used to analyze the number of chocolate chip parts per cookie in the following problem?The quality control manager of Marilyns Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 6.0. The manager is interested in analyzing the probability that any particular cookie being inspected has fewer than 5.0 chip parts.a) binomial distribution.b) Poisson distribution.c) normal distribution.d) none of the above.ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: Poisson distribution, properties15. 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) normal distribution.d) none of the above.ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: Poisson distribution, properties16. 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) normal distribution.d) none of the above.ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: binomial distribution, properties17. 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) normal distribution.d) none of the above.ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: Poisson distribution, properties18. 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) normal distribution.d) none of the above.ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: binomial distribution, properties19. 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 average cost for all weekly rat purchases is $13.00.d) The rat cost that occurs more often than any other is $13.00.ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: mean20. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution:Price:$10.00$12.50$15.00Probability:0.350.400.25How much should the lab budget for next years rat orders be, assuming this distribution does not change?a) $520b) $637c) $650d) $780ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: mean, probability distribution21. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.a) The number of tickets that is written most often is 6.5 tickets per day.b) Half of the days have less than 6.5 tickets written and half of the days have more than 6.5 tickets written.c) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day.d) The mean has no interpretation since 0.5 ticket can never be written.ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: mean, Poisson distribution22. True or False: The Poisson distribution can be used to model a continuous random variable.ANSWER:FalseTYPE: TF DIFFICULTY: EasyKEYWORDS: Poisson distribution, properties23. True or False: Another name for the mean of a probability distribution is its expected value.ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: mean24. True or False: The number of customers arriving at a department store in a 5-minute period has a binomial distribution.ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties25. True or False: The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties26. True or False: The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: binomial distribution, properties27. True or False: The diameters of 10 randomly selected bolts have a binomial distribution.ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: binomial distribution, properties28. True or False: The largest value that a Poisson random variable X can have is n.ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties29. True or False: In a Poisson distribution, the mean and standard deviation are equal.ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties30. True or False: In a Poisson distribution, the mean and variance are equal.ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 31. True or False: If p remains constant in a binomial distribution, an increase in n will increase the variance.ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: binomial distribution, properties32. True or False: If p remains constant in a binomial distribution, an increase in n will not change the mean.ANSWER:FalseTYPE: TF DIFFICULTY: ModerateKEYWORDS: binomial distribution, properties33. True or False: Suppose that a judges decisions follow a binomial distribution and that his verdict is correct 90% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: binomial distribution, probability34. True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.0504.ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: Poisson distribution, probabilityTABLE 5-1The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.35. Referring to Table 5-1, the probability that both sound an alarm in the presence of smoke is _.ANSWER:0.64TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution36. Referring to Table 5-1, the probability that neither sound an alarm in the presence of smoke is _.ANSWER:0.04TYPE: FI DIFFICULTY: ModerateKEYWORDS: binomial distribution 37. Referring to Table 5-1, the probability that at least one sounds an alarm in the presence of smoke is _.ANSWER:0.96TYPE: FI DIFFICULTY: Difficult KEYWORDS: binomial distributionTABLE 5-2A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). 38. Referring to Table 5-2, the probability that all 3 businesses succeed is _.ANSWER:0.216TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution39. Referring to Table 5-2, the probability that all 3 businesses fail is _.ANSWER:0.064TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution40. Referring to Table 5-2, the probability that at least 1 business succeeds is _.ANSWER:0.936TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution41. Referring to Table 5-2, the probability that exactly 1 business succeeds is _.ANSWER:0.288TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution42. If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = _ .ANSWER:0.4116TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution43. If X has a binomial distribution with n = 4 and p = 0.3, then P(X 1) = _ .ANSWER:0.3483TYPE: FI DIFFICULTY: ModerateKEYWORDS: binomial distribution44. If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = _ .ANSWER:0.0729TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution45. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 1 prefers brand C is _. ANSWER:0.0768TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution46. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that at least 1 prefers brand C is _. ANSWER:0.9898TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution47. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 3 prefer brand C is _. ANSWER:0.3456TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution48. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 4 prefer brand C is _.ANSWER:0.2592TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution49. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that at most 2 prefer brand C is _. ANSWER:0.3174TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution50. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that more than 3 prefer brand C is _.ANSWER:0.3370TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution51. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that less than 2 prefer brand C is _.ANSWER:0.0870TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution52. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The average number that you would expect to prefer brand C is _.ANSWER:3TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, mean53. Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The variance of the number that prefer brand C is _.ANSWER:1.2TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, varianceTABLE 5-3The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media. X0123P(X)0.350.350.250.0554. Referring to Table 5-3, the probability of no retransmissions is _.ANSWER:0.35TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution55. Referring to Table 5-3, the probability of at least one retransmission is _.ANSWER:0.65TYPE: FI D