Quantitative Analysis for Management 13th Edition Test Bank

Quantitative Analysis for Management, 13e (Render et al.) Chapter 2 Probability Concepts and Applications 1) Subjective probability implies that we can measure the relative frequency of the values of the random variable. Answer: FALSE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 2) Mutually exclusive events exist if only one of the events can occur on any one trial. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 3) Stating that two events are statistically independent means that the probability of one event occurring is independent of the probability of the other event having occurred. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 4) Saying that a set of events is collectively exhaustive implies that one of the events must occur. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 5) Saying that a set of events is mutually exclusive and collectively exhaustive implies that one and only one of the events can occur on any trial. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 6) A posterior probability is a revised probability. Answer: TRUE Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Concept 7) Bayes’ theorem enables us to calculate the probability that one event takes place knowing that a second event has or has not taken place. Answer: TRUE Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Concept 8) A probability density function is a mathematical way of describing Bayes’ theorem. Answer: FALSE Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Concept 9) If two events are mutually exclusive, the probability of both events occurring is simply the sum of the individual probabilities. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 10) Given two statistically dependent events (A,B), the conditional probability of P(A|B) = P(B)/P(AB). Answer: FALSE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 11) Given two statistically independent events (A,B), the joint probability of P(AB) = P(A) + P(B). Answer: FALSE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 12) Given two statistically independent events (A,B), the conditional probability P(A|B) = P(A). Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 13) Suppose that you enter a drawing by obtaining one of 20 tickets that have been distributed. By using the classical method, you can determine that the probability of your winning the drawing is 0.05. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 14) Assume that you have a box containing five balls: two red and three white. You draw a ball two times, each time replacing the ball just drawn before drawing the next. The probability of drawing only one white ball is 0.20. Answer: FALSE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 15) If we roll a single die twice, the probability that the sum of the dots showing on the two rolls equals four (4), is 1/6. Answer: FALSE Diff: Difficult Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 16) Consider a standard 52-card deck of cards. The probability of drawing either a seven or a black card is 7/13. Answer: TRUE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 17) Although one revision of prior probabilities can provide useful posterior probability estimates, additional information can be gained from performing the experiment a second time. Answer: TRUE Diff: Moderate Topic: FURTHER PROBABILITY REVISIONS LO: 2.3: Use Bayes’ Theorem to establish further probability revisions. AACSB: Analytical thinking Classification: Concept 18) The joint probability of two or more independent events occurring is the sum of their marginal or simple probabilities. Answer: FALSE Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 19) The number of bad checks written at a local store is an example of a discrete random variable. Answer: TRUE Diff: Moderate Topic: RANDOM VARIABLES LO: 2.4: Describe and provide examples of both discrete and continuous random variables. AACSB: Application of knowledge Classification: Concept 20) Given the following distribution: Outcome A B C D Value of Random Variable Probability 1 .4 2 .3 3 .2 4 .1 The expected value is 3. Answer: FALSE Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 21) A new young executive is perplexed at the number of interruptions that occur due to employee relations. She has decided to track the number of interruptions that occur during each hour of her day. Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day. The data is shown below. Number of Interruptions in 1 hour 0 interruption 1 interruptions 2 interruptions 3 interruptions Probability .5 .3 .1 .1 On average, she should expect 0.8 interruptions per hour. Answer: TRUE Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 22) A new young executive is perplexed at the number of interruptions that occur due to employee relations. She has decided to track the number of interruptions that occur during each hour of her day. Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day. The data is shown below. Number of Interruptions in 1 hour 0 interruption 1 interruptions 2 interruptions 3 interruptions Probability .4 .3 .2 .1 On average, she should expect 1.0 interruptions per hour. Answer: TRUE Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 23) The expected value of a binomial distribution is expressed as np, where n equals the number of trials and p equals the probability of success of any individual trial. Answer: TRUE Diff: Moderate Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Concept 24) The standard deviation equals the square of the variance. Answer: FALSE Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Concept 25) The probability of obtaining specific outcomes in a Bernoulli process is described by the binomial probability distribution. Answer: TRUE Diff: Moderate Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Concept 26) The variance of a binomial distribution is expressed as np/(1 – p), where n equals the number of trials and p equals the probability of success of any individual trial. Answer: FALSE Diff: Moderate Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Concept 27) The F distribution is a continuous probability distribution that is helpful in testing hypotheses about variances. Answer: TRUE Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Concept 28) The mean and standard deviation of the Poisson distribution are equal. Answer: FALSE Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 29) In a normal distribution, the Z value represents the number of standard deviations from a value X to the mean. Answer: TRUE Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Concept 30) Assume you have a normal distribution representing the likelihood of completion times. The mean of this distribution is 10, and the standard deviation is 3. The probability of completing the project in 8 or fewer days is the same as the probability of completing the project in 18 days or more. Answer: FALSE Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 31) The F statistic is the ratio of two sample standard deviations from independent normal distributions. Answer: FALSE Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Concept 32) Assume you have a normal distribution representing the likelihood of completion times. The mean of this distribution is 10, and the standard deviation is 3. The probability of completing the project in 7 or fewer days is the same as the probability of completing the project in 13 days or more. Answer: TRUE Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 33) Subjective probability assessments depend on A) the total number of trials. B) the relative frequency of occurrence. C) the number of occurrences of the event. D) experience and judgment. Answer: D Diff: Easy Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 34) A conditional probability P(B|A) is equal to its marginal probability P(B) if A) it is a joint probability. B) statistical dependence exists. C) statistical independence exists. D) the events are mutually exclusive. Answer: C Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 35) Suppose that we determine the probability of a warm winter based on the number of warm winters experienced over the past 10 years. In this case, we have used A) relative frequency. B) the classical method. C) the logical method. D) subjective probability. Answer: A Diff: Easy Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 36) Bayes’ theorem is used to calculate A) revised probabilities. B) joint probabilities. C) prior probabilities. D) subjective probabilities. Answer: A Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Concept 37) If the sale of ice cream and pizza are independent, then as ice cream sales decrease by 60 percent during the winter months, pizza sales will A) increase by 60 percent. B) increase by 40 percent. C) decrease by 40 percent. D) be unrelated. Answer: D Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 38) If P(A) = 0.3, P(B) = 0.2, P(A and B) = 0.0, what can be said about events A and B? A) They are independent. B) They are mutually exclusive. C) They are posterior probabilities. D) They are collectively exhaustive. Answer: B Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 39) Suppose that 10 golfers enter a tournament and that their respective skill levels are approximately the same. What is the probability that one of the first three golfers that registered for the tournament will win? A) 0.100 B) 0.001 C) 0.300 D) 0.299 Answer: C Diff: Easy Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 40) Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same. Six of the entrants are female and two of those are engineering majors. Three of the men are engineers. What is the probability that the winner will be either female or majoring in something other than engineering? A) 0.10 B) 0.30 C) 0.70 D) 0.90 Answer: C Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 41) Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same. Six of the entrants are female and two of those are engineering majors. Three of the men are engineers. What is the probability that the winner will be a male engineering major? A) 0.10 B) 0.30 C) 0.70 D) 0.90 Answer: B Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 42) Suppose that 10 sophomores enter a belching contest and that their respective skill levels are approximately the same. Six of the entrants are female and two of those are engineering majors. Three of the men are engineers. What is the probability that the winner will be either a nonengineering major or a male? A) 0.20 B) 0.40 C) 0.60 D) 0.80 Answer: D Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 43) “The probability of event B, given that event A has occurred” is known as a ________ probability. A) continuous B) marginal C) simple D) conditional Answer: D Diff: Easy Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 44) When does P(A|B) = P(A)? A) when A and B are mutually exclusive B) when A and B are statistically independent C) when A and B are statistically dependent D) when A and B are collectively exhaustive Answer: B Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 45) A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to “win” the tickets. There are 6 secretaries, 5 consultants and 4 partners in the firm. Which of the following statements is not true? A) The probability of a secretary winning a ticket on the first draw is 6/15. B) The probability of a secretary winning a ticket on the second draw given that a consultant won a ticket on the first draw is 6/15. C) The probability of a consultant winning a ticket on the first draw is 1/3. D) The probability of two secretaries winning both tickets is 1/7. Answer: B Diff: Difficult Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 46) A consulting firm has received 2 Super Bowl playoff tickets from one of its clients. To be fair, the firm is randomly selecting two different employee names to “win” the tickets. There are 6 secretaries, 5 consultants, and 4 partners in the firm. Which of the following statements is true? A) The probability of a partner winning on the second draw given that a partner won on the first draw is 3/14. B) The probability of a secretary winning on the second draw given that a secretary won on the first draw is 2/15. C) The probability of a consultant winning on the second draw given that a consultant won on the first draw is 5/14. D) The probability of a partner winning on the second draw given that a secretary won on the first draw is 8/30. Answer: A Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 47) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is either enrolled in accounting or statistics, but not both? A) 0.45 B) 0.50 C) 0.40 D) 0.05 Answer: C Diff: Difficult Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 48) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is enrolled in accounting? A) 0.20 B) 0.25 C) 0.30 D) 0.50 Answer: C Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 49) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is enrolled in statistics? A) 0.05 B) 0.20 C) 0.25 D) 0.30 Answer: B Diff: Easy Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 50) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is enrolled in both statistics and accounting? A) 0.05 B) 0.06 C) 0.20 D) 0.25 Answer: A Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 51) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random and found to be enrolled in statistics, what is the probability that the student is also enrolled in accounting? A) 0.05 B) 0.30 C) 0.20 D) 0.25 Answer: D Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 52) Suppose that when the temperature is between 35 and 50 degrees, it has historically rained 40% of the time. Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days. You have scheduled a golf tournament for April 12. What is the probability that players will experience rain and a temperature between 35 and 50 degrees? A) 0.333 B) 0.400 C) 0.833 D) 0.480 Answer: A Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 53) Suppose that, historically, April has experienced rain and a temperature between 35 and 50 degrees on 20 days. Also, historically, the month of April has had a temperature between 35 and 50 degrees on 25 days. You have scheduled a golf tournament for April 12. If the temperature is between 35 and 50 degrees on that day, what will be the probability that the players will get wet? A) 0.333 B) 0.667 C) 0.800 D) 1.000 Answer: C Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 54) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is enrolled in neither accounting nor statistics? A) 0.45 B) 0.50 C) 0.55 D) 0.05 Answer: C Diff: Difficult Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 55) At a university with 1,000 business majors, there are 200 business students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, what is the probability that the student is not enrolled in statistics? A) 0.05 B) 0.20 C) 0.25 D) 0.80 Answer: D Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 56) A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that the second item will be defective? A) 0.05 B) 0.005 C) 0.18 D) 0.20 Answer: A Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 57) A production process is known to produce a particular item in such a way that 5 percent of these are defective. If two items are randomly selected as they come off the production line, what is the probability that both are defective (assuming that they are independent)? A) 0.0100 B) 0.1000 C) 0.2000 D) 0.0025 Answer: D Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 58) A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product is actually not successful? A) 0.63 B) 0.06 C) 0.07 D) 0.24 Answer: B Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 59) A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate an unsuccessful market for the product and the product is actually successful? A) 0.63 B) 0.06 C) 0.07 D) 0.24 Answer: C Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 60) A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate an unsuccessful market for the product and the product is actually unsuccessful? A) 0.63 B) 0.06 C) 0.07 D) 0.24 Answer: D Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 61) A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful, and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the product will be successful if the market research indicates a success? A) 0.10 B) 0.90 C) 0.91 D) 0.63 Answer: C Diff: Difficult Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 62) A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of their customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability a customer uses both services? A) 0.12 B) 0.60 C) 0.36 D) 0.24 Answer: C Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 63) A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of the existing customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability that a customer uses only one of these services? A) 0.40 B) 0.60 C) 0.48 D) 0.24 Answer: C Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 64) A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge. Management believes 60 percent of the existing customers will take advantage of this service. They are also considering offering customers the option of opening an account and receiving monthly bills. They believe 60 percent of customers (regardless of whether or not they use the pick-up service) will use the account service. If the two services are introduced to the market, what is the probability a customer uses neither of these services? A) 0.16 B) 0.24 C) 0.80 D) 0.36 Answer: A Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 65) Which distribution is helpful in testing hypotheses about variances? A) binomial distribution B) distribution C) normal distribution D) Poisson distribution Answer: B Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Concept 66) A company is considering producing two new electronic games designed for the popular Gameboy toy. Based on market data, management believes that there is a 60 percent chance that a “cops and robbers” game will be successful and a 40 percent chance that a “let’s play house” game will be successful. As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other. If two products are introduced to the market, what is the probability that both are successful? A) 0.12 B) 0.60 C) 0.36 D) 0.24 Answer: D Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 67) A company is considering producing two new electronic games designed for the popular Gameboy toy. Based on market data, management believes that there is a 60 percent chance that a “cops and robbers” game will be successful and a 40 percent chance that a “let’s play house” game will be successful. As these products are completely different, it may be assumed that the success of one is totally independent of the success of the other. If two products are introduced to the market, what is the probability that both are failures? A) 0.16 B) 0.24 C) 0.80 D) 0.36 Answer: B Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 68) A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the results indicate a successful market for the product and the product actually is successful? A) 0.90 B) 0.54 C) 0.60 D) 0.63 Answer: D Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 69) The expected value of a probability distribution is A) the measure of the spread of the distribution. B) the variance of the distribution. C) the average value of the distribution. D) the probability density function. Answer: C Diff: Easy Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Concept 70) Which of the following is not true for discrete random variables? A) The expected value is the weighted average of the values. B) They can assume only a countable number of values. C) The probability of each value of the random variable must be 0. D) The probability values always sum up to 1. Answer: C Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Concept 71) The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, or 2. The probabilities are the same for each of these (1/3). If X is the number of calls arriving in a five-minute time period, what is the mean of X? A) 1/3 B) 2/3 C) 1 D) 4/3 Answer: C Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 72) The number of phone calls coming into a switchboard in the next five minutes will either be 0, 1, 2, 3, 4, 5, or 6. The probabilities are the same for each of these (1/7). If X is the number of calls arriving in a five-minute time period, what is the mean of X? A) 2 B) 3 C) 4 D) 5 Answer: B Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 73) A discrete random variable has a mean of 400 and a variance of 64. What is the standard deviation? A) 64 B) 8 C) 20 D) 400 Answer: B Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 74) Which of the following is not true about continuous random variables? A) They have an infinite set of values. B) The area under each of the curves represents probabilities. C) The entire area under each of the curves equals 1. D) They can only be integer values. Answer: D Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Concept 75) Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that exactly 2 customers would be willing to switch their cable? A) 0.1 B) 0.04 C) 0.137 D) 0.206 Answer: C Diff: Difficult Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Application 76) Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that no more than 3 customers would be willing to switch their cable? A) 0.85 B) 0.15 C) 0.20 D) 0.411 Answer: D Diff: Difficult Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Application 77) Historical data indicates that only 20% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that between 2 and 5 (inclusive) customers are willing to switch companies? A) 0.1369 B) 0.1746 C) 0.0377 D) 0.7350 Answer: D Diff: Difficult Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Application 78) Properties of the normal distribution include A) a continuous bell-shaped distribution. B) a discrete probability distribution. C) the number of trials is known and is either 1, 2, 3, 4, 5, etc. D) the random variable can assume only a finite or limited set of values. Answer: A Diff: Easy Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Concept 79) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses fewer than 600 minutes? A) 0 B) 0.023 C) 0.841 D) 0.977 Answer: D Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 80) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses fewer than 400 minutes? A) 0 B) 0.023 C) 0.159 D) 0.977 Answer: B Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 81) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses more than 350 minutes? A) 0.001 B) 0.999 C) 0.618 D) 0.382 Answer: B Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 82) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses more than 580 minutes? A) 0.152 B) 0.0548 C) 0.848 D) 0.903 Answer: B Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 83) The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses between 400 and 500 minutes? A) 0.4773 B) 0.05228 C) 0.0228 D) 0.9773 Answer: A Diff: Difficult Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 84) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average price per square foot for a home is greater than $110? A) 0 B) 0.023 C) 0.841 D) 0.977 Answer: B Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 85) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average price per square foot for a home is greater than $90? A) 0 B) 0.023 C) 0.159 D) 0.977 Answer: D Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 86) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average price per square foot for a home is less than $85? A) 0.001 B) 0.999 C) 0.618 D) 0.382 Answer: A Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 87) Data for a particular subdivision near downtown Houston indicate that the average price per square foot for a home is $100 with a standard deviation of $5 (normally distributed). What is the probability that the average price per square foot for a home is less than $108? A) 0.152 B) 0.097 C) 0.848 D) 0.945 Answer: D Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 88) The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks. The construction company must pay a penalty if the project is not finished by the due date in the contract. If a construction company bidding on this contract puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty? A) 0 B) 1.000 C) 0.500 D) 1/8 Answer: C Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 89) The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks. The construction company must pay a penalty if the project is not finished by the due date in the contract. If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, what due date (project week #) should be negotiated? A) 81.28 B) 92.8 C) 81.82 D) .81954 Answer: B Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 90) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take less than 40 minutes? A) 0.50 B) 0.20 C) 0.80 D) 1.00 Answer: A Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 91) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take less than 35 minutes? A) 0.84134 B) 0.15866 C) 0.53983 D) 0.46017 Answer: B Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 92) The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take more than 40 minutes? A) 0.2500 B) 0.0625 C) 1.000 D) 0.5000 Answer: D Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 93) Queuing Theory makes use of the A) normal probability distribution. B) uniform probability distribution. C) binomial probability distribution. D) Poisson probability distribution. Answer: D Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 94) The number of cars passing through an intersection in the next five minutes can usually be described by the A) normal distribution. B) uniform distribution. C) exponential distribution. D) Poisson distribution. Answer: D Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 95) Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. What is the probability that in the next hour there will be exactly 12 arrivals? A) 0.0000 B) 0.0661 C) 0.7500 D) 0.1322 Answer: B Diff: Difficult Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 96) The number of calls received by call center follows a Poisson process with a rate of 1.5 per minute. What is the probability that a minute goes by without a call? A) 0 B) 0.223 C) 0.500 D) 0.558 E) 1 Answer: B Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 97) Which of the following statements concerning the F distribution is true? A) The F distribution is discrete. B) The F distribution is symmetrical. C) The F distribution is useful in modeling customer arrivals. D) The F distribution is useful in testing hypotheses about variance. Answer: D Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Concept 98) What is the F value associated with α = 0.05, numerator degrees of freedom (df1) equal to 4, and denominator degrees of freedom (df2) equal to 9? A) 3.63 B) 1.80 C) 6.0 D) 0.11 Answer: A Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 99) Given a df1 = 3 and df2 = 6, what is the probability that F is greater than 4.3? A) 0.0610 B) 0.1294 C) 0.05 D) 0.5 Answer: A Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 100) What is the probability that F is between 4 and 5, given a df1 = 4 and df2 = 6? A) 0.0654 B) 0.0406 C) 0.0248 D) 0.05 Answer: C Diff: Difficult Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 101) Which of the following characteristics is not true for the exponential distribution? A) It is discrete probability distribution. B) It is also called the negative exponential distribution. C) It is used in dealing with queuing problems. D) It is used to describe the times between customer arrivals. Answer: A Diff: Moderate Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 102) The length of time that it takes the tollbooth attendant to service each driver can typically be described by the A) normal distribution. B) uniform distribution. C) exponential distribution. D) Poisson distribution. Answer: C Diff: Moderate Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 103) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute) when it comes to license renewals. The service time follows an exponential distribution. What is the probability that it will take less than 2 minutes for a particular customer to get a license renewal? A) 1 B) 0.487 C) 0.513 D) 0 Answer: B Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 104) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute) when it comes to license renewals. The service time follows an exponential distribution. What is the probability that it will take less than 3 minutes for a particular customer to get a license renewal? A) 0.5 B) 0 C) 1 D) 0.368 Answer: D Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 105) The Department of Motor Vehicles (DMV) can service customers at a rate of 20 per hour (or 1/3 per minute) when it comes to license renewals. The service time follows an exponential distribution. What is the probability that it will take between 2 and 3 minutes to be served? A) 0.4831 B) 0 C) 1 D) 0.1419 Answer: D Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 106) Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that it will take less than 1/2 of a minute between consecutive drivers? A) 0.167 B) 0.223 C) 0.777 D) 0.5 Answer: C Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 107) Drivers arrive at a toll booth at a rate of 3 per minute during peak traffic periods. The time between consecutive driver arrivals follows an exponential distribution. What is the probability that it will take more than 1/3 of a minute between consecutive drivers? A) 0.632 B) 0.111 C) 0.368 D) 0.208 Answer: C Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 108) Which of these suggests a discrete random variable? A) the exact time it takes to run a mile B) the exact number of registered voters in your state C) the exact amount of blood in a human body D) the lifetime of a CF light bulb Answer: B Diff: Moderate Topic: RANDOM VARIABLES LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 109) Which of these suggests a continuous random variable? A) the roll of a fair die B) the number of dollar bills in your wallet C) the number of parking permits issued at your school D) the lifetime of an incandescent light bulb Answer: D Diff: Moderate Topic: RANDOM VARIABLES LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 110) A random variable A) is normally represented by an operator such as ≤ or ≥. B) can be simultaneously continuous and discrete. C) assigns a real number to every possible outcome or event in an experiment. D) must represent only numerical values. Answer: C Diff: Moderate Topic: RANDOM VARIABLES LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 111) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the disease is not present in any particular person? A) 0.990 B) 0.960 C) 0.995 D) 0.950 Answer: C Diff: Easy Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 112) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the disease is present if the test result comes back positive? A) 0.1106 B) 0.8894 C) 0.9600 D) 0.0400 Answer: A Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 113) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result comes back positive if the disease is present? A) 0.8894 B) 0.9500 C) 0.9600 D) 0.9900 Answer: A Diff: Easy Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 114) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result comes back negative if the disease is present? A) 0.89 B) 0.01 C) 0.96 D) 0.04 Answer: B Diff: Easy Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 115) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result comes back negative regardless of whether the disease is present? A) 0.9553 B) 0.8994 C) 0.9999 D) 0.9762 Answer: A Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 116) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the disease is absent if the test result is negative? A) 0.9553 B) 0.8994 C) 0.9999 D) 0.9762 Answer: C Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 117) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result is negative if the disease is absent? A) 0.95 B) 0.96 C) 0.99 D) 0.995 Answer: B Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 118) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result is positive if the disease is absent? A) 0.01 B) 0.05 C) 0.055 D) 0.04 Answer: D Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 119) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the disease is not present if the test result is positive? A) 0.8894 B) 0.9900 C) 0.9500 D) 0.9763 Answer: A Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 120) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the disease is present if the test result is negative? A) 0.005 B) 0.0001 C) 0.0010 D) 0.0005 Answer: B Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 121) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the test result is positive? A) 0.0056 B) 0.0523 C) 0.0448 D) 0.1106 Answer: C Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 122) An urn contains 7 blue and 3 yellow chips. If the drawing of chips is done with replacement, determine the probability of: (a) drawing three yellow chips. (b) drawing a blue chip on the first draw and a yellow chip on the second draw. (c) drawing a blue chip on the second draw given that a yellow chip was drawn on the first draw. (d) drawing a yellow chip on the second draw given that a blue chip was drawn on the first draw. (e) drawing a yellow chip on the second draw given that a yellow chip was drawn on the first draw. Answer: (a) 0.027 (b) 0.210 (c) 0.700 (d) 0.300 (e) 0.300 Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 123) A market research study is being conducted to determine if a product modification will be well received by the public. A total of 1,000 consumers are questioned regarding this product. The table below provides information regarding this sample. Male Female Positive Reaction 240 260 Neutral Negative Reaction Reaction 60 100 220 120 (a) What is the probability that a randomly selected male would find this change unfavorable (negative)? (b) What is the probability that a randomly selected person would be a female who had a positive reaction? (c) If it is known that a person had a negative reaction to the study, what is the probability that the person is male? Answer: (a) 100/400 = 0.25 (b) 260/1000 = 0.260 (c) 100/220 = 0.4545 Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 124) In a production run of 300 units, there are exactly 20 defective items and 280 good items. (a) What is the probability that a randomly selected item is defective? (b) If two items are sampled without replacement, what is the probability that both are good? (c) If two items are randomly sampled without replacement, what is the probability that the first is good but the second is defective? Answer: (a) 20/300 = 0.067 (b) (280/300)(279/299) = 0.871 (c) (280/300)(20/299) = 0.062 Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 125) A new television program was viewed by 200 people (120 females and 80 males). Of the females, 60 liked the program and 60 did not. Of the males, 60 of the 80 liked the program. (a) What is the probability that a randomly selected individual liked the program? (b) If a male in this group is selected, what is the probability that he liked the program? (c) What is the probability that a randomly selected individual is a female and liked the program? Answer: (a) 120/200 = 0.60 (b) 60/80 = 0.75 (c) 60/200 = 0.30 Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 126) Colonel Motors (an automobile company) has prepared a marketing campaign for its bestselling car. The focus of the campaign is quality, and it is claimed that 97 percent of the purchasers of this car have no complaints in the first year. You and your sister Kim have each purchased one of these cars. (a) What is the probability that neither of you has a complaint about the car in the first year if the advertising claim is true? (b) What is the probability that exactly one of you has a complaint about the car in the first year if the advertising claim is true? Answer: (a) 0.97(0.97) = 0.9409 (b) 0.03(0.97) + 0.97(0.03) = 0.0582 Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 127) A local “home TV repair service” company has two repairmen who make all of the home repairs. The company sends Repairman D on 70 percent of all jobs, because the likelihood of a “second follow-up call” within a week is only 0.08 compared to 0.20 for Repairman K. If you had a recent repair job that is going to require a second follow-up call, what is the probability that Repairman K did your initial repair work? Answer: P(K|2nd) = 0.06/(.06 + .056) = 0.517 Diff: Difficult Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 128) Our department store is having a sale on personal computers, of which three are in stock (no rain checks). There is a certain probability of selling none. The probability of selling one is twice as great as the probability of selling none. The probability of selling two is three times the probability of selling none. Finally, the probability of selling all the personal computers is four times as great as the probability of selling none. In a table, list the outcomes and their probabilities. Hint: Let the probability of selling none equal x. Answer: Outcome Probability Sell 0 0.1 Sell 1 0.2 Sell 2 0.3 Sell 3 0.4 Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 129) ABC Manufacturing has 6 machines that perform a particular task. Breakdowns occur frequently for this machine. Past records indicate that the number of breakdowns that occur each day is described by the following probability distribution: Number of Breakdowns 0 1 2 3 More than 3 Probability 0.4 0.3 0.2 0.1 0.0 a. What is the expected number of breakdowns in any given day? b. What is the variance for this distribution? c. What is the probability that there will be at least 2 breakdowns in a day? Answer: a. expected value = 1.0 b. variance = 1(.4) + 0(.3) + 1(.2) + 4(.1) = 1.0 c. P(2 or more) = 0.2 + 0.1 = 0.3 Diff: Moderate Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 130) Fast Service Store has maintained daily sales records on the various size “Cool Drink” sales. “Cool Drink” Price $0.50 $0.75 $1.00 $1.25 Total Number Sold 75 120 125 80 400 Assuming that past performance is a good indicator of future sales, (a) What is the probability of a customer purchasing a $1.00 “Cool Drink?” (b) What is the probability of a customer purchasing a $1.25 “Cool Drink?” (c) What is the probability of a customer purchasing a “Cool Drink” that costs greater than or equal to $1.00? (d) What is the expected value of a “Cool Drink”? (e) What is the variance of a “Cool Drink”? Answer: (a) 125/400 = 0.3125 (b) 80/400 = 0.20 (c) 205/400 = 0.5125 (d) .5(.1875) + .75(.3) + 1(.3125) + 1.25(.2) = .88125 (e) 0.064 Diff: Difficult Topic: PROBABILITY DISTRIBUTIONS LO: 2.5: Explain the difference between discrete and continuous probability distributions. AACSB: Analytical thinking Classification: Application 131) In a given office, the color printer breaks down with a probability of 20% in any month. A binomial process is assumed for a period of 10 months. (a) What is the probability that the printer breaks down exactly 2 times? (b) What is the probability that the printer breaks down at most 1 time? (c) What is the probability that the printer breaks down more than once? Answer: (a) P(r = 2) = 0.3020 (b) P(r ≤ 1) = 0.3758 (c) P(r > 1) = 0.6242 Diff: Difficult Topic: THE BINOMIAL DISTRIBUTION LO: 2.6: Understand the binomial distribution. AACSB: Analytical thinking Classification: Application 132) The number of defects that occur per unit of product follows a Poisson distribution with a mean of 4 defects per unit. What is the standard deviation of this distribution? Answer: 2 Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 133) Machine breakdowns occur at a rate of 0.4 per week. The time between breakdowns follows an exponential distribution. What is the probability that more than 2 weeks go by without a breakdown? Answer: 0.4493 Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 134) Compute the F value based on the following: (a) df1 = 2, df2 = 4, α = 0.01 (b) df1 = 3 df2 = 6, α = 0.05 Answer: (a) 18 (b) 4.76 Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 135) For df1 = 3 and df2 = 7, what is the probability that F is greater than 5? Answer: 0.0367 Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 136) For df1 = 4 and df2 = 5, what is the probability that F is greater than 4.5? Answer: 0.06515 Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 137) A call center receives calls from customers at a rate of 2 per min. The time between customer calls follows an exponential distribution. (a) What is the probability that it takes 1/3 of a minute or less between consecutive customer calls? (b) What is the probability that it takes 1/2 of a minute or more between consecutive customer calls? Answer: (a) 0.487 (b) 0.368 Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 138) Customer arrivals occur at a rate of 1.2 per minute. The time between customer arrivals follows an exponential distribution. What is the probability that it takes between 1 and 2 minutes between customer arrivals? Answer: 0.2105 Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 139) Arrivals in a university advising office during the week of registration are known to follow a Poisson distribution with an average of 4 people arriving each hour. (a) What is the probability that exactly 4 people will arrive in the next hour? (b) What is the probability that exactly 5 people will arrive in the next hour? Answer: (a) P(X = 4) = 0.1954 (b) P(X = 5) = 0.1563 Diff: Difficult Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 140) Explain why event probabilities range from 0 to 1. Answer: The number 0 represents no chance of occurrence, while 1 represents a 100 percent chance of occurrence. Any number between 0 and 1 represents that particular event’s chance of occurrence. Any negative number or number exceeding 1 has no meaning for an event probability. Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Reflective thinking Classification: Application 141) Using a standard deck of 52 cards, explain why the situation of drawing a 7 and a club is not collectively exhaustive. Answer: It is possible to draw other cards that are non-clubs and also not a 7. Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 142) If two events (A,B) are mutually exclusive, what is the probability of event A or event B occurring? Answer: P(A or B) = P(A) + P(B) Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Application 143) If two events (A,B) are not mutually exclusive, what is the probability of event A or event B occurring? Answer: P(A or B) = P(A) + P(B) – P(A and B) Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 144) If two events (A,B) are independent, what is their joint probability? Answer: P(AB) = P(A) × P(B) Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 145) If two events (A,B) are dependent, what is the conditional probability of P(A|B)? Answer: P(A|B) = P(AB)|P(B) Diff: Moderate Topic: FUNDAMENTAL CONCEPTS LO: 2.1: Understand the basic foundations of probability analysis. AACSB: Analytical thinking Classification: Concept 146) In what way is the F distribution often used? Answer: It is helpful in testing hypotheses about variances. Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Concept 147) What are the parameter(s) of the Poisson distribution? What is the ratio of these parameters? Answer: The parameters are the mean and the variance λ; their ratio is 1. Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 148) What is the relationship between the exponential distribution and the Poisson distribution? Answer: The exponential and Poisson distributions may be expressed as inverses of each other. If the number of occurrences per time period follows a Poisson distribution, then the time between those occurrences follows an exponential distribution. Diff: Moderate Topic: THE POISSON DISTRIBUTION LO: 2.10: Understand the Poisson distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Concept 149) Disco Fever is randomly found in one half of one percent of the general population. Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease. The test also yields a false-positive in 4% of the cases where the disease is not present. What is the probability that the disease is present if the test result is positive? Answer: .1106 Diff: Moderate Topic: REVISING PROBABILITIES WITH BAYES’ THEOREM LO: 2.2: Use Bayes’ Theorem to establish posterior probabilities. AACSB: Analytical thinking Classification: Application 150) Customer arrivals are exponentially distributed and occur on average every 10 minutes. What is the standard deviation of customer interarrival times? Answer: 3.162 Diff: Difficult Topic: THE EXPONENTIAL DISTRIBUTION LO: 2.9: Understand the exponential distribution and its relation to queuing theory. AACSB: Analytical thinking Classification: Application 151) For df1 = 34 and df2 = 15, what value of the F-statistic is required such that P(F>f) = 0.1? Answer: 1.86 Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 152) For df1 = 34 and df2 = 5, what value of the F-statistic is required such that P(F>f) = 0.001? Answer: 24.74 Diff: Moderate Topic: THE F DISTRIBUTION LO: 2.8: Understand the F distribution AACSB: Analytical thinking Classification: Application 153) Michael’s arms windmilled, propelling him through the water at a pace few could believe. He completed his 100 meter butterfly in 49.82 seconds and was pleased with his performance. At the ceremony later that afternoon, Michael and the other seven finalists were awarded participation medals, which he found distressing. He was quick to point out that the average time for the 100 meter butterfly was 53 seconds with a standard deviation of 0.9 seconds. There must be some way of demonstrating how exceptional his time was, so he turned to his friend who was studying quantitative analysis to help him prove this. How exceptional is Michael’s performance? Answer: The Z score for his 49.82 is -3.5333 and the probability of seeing a lower time is 0.000205. Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 154) “It’s 75 degrees and sunny here in San Diego this afternoon…,” the weatherman droned on, repeating a phrase that probably should have been recorded and played on an endless loop. Tim looked at the previous year’s high temperatures and noted that the average was 75 degrees with a standard deviation of 2.5 degrees and approximated a normal distribution. Armed with this evidence, determine: (a) the probability of a daily temperature between 79 degrees F and 85 degrees F. (b) the probability that the daily temperature exceeds 80 degrees F. (c) the probability that the daily temperature is below 74 degrees F. Answer: (a) P(79 < X 80) = 0.02275 (c) P(X < 74) = 0.345 Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application 155) An MBA director has decided to improve the profile of her program by admitting only the finest students. After an exhaustive search on the internet, she learns that combined GMAT scores average 550 with a standard deviation of 130. (a) What cutoff score should she establish if she wants to consider only applicants scoring in the top 5%? (b) If she uses 700 as her minimum score, what percentile can she claim for her incoming class' performance on the GMAT? (c) If 1000 test takers apply, would she expect to find more students with scores in the range of 500 to 600 or in the range of 50 to 450? (Assume that applicants can actually score a 50 on the GMAT.) Answer: (a) 95th percentile is 763 (b) a 700 is the 88th percentile (c) P(500 < X < 600) = 0.299, P(50 < X < 450) = 0.221 — she would expect 78 more applications in the 500 to 600 pile than in the 50 to 450 pile. Diff: Moderate Topic: THE NORMAL DISTRIBUTION LO: 2.7: Understand the normal distribution and use the normal table. AACSB: Analytical thinking Classification: Application