Download 182.88 Kb.

Introduction to Management Science, 10e (Taylor) Chapter 11 Probability and Statistics 1) Deterministic techniques assume that no uncertainty exists in model parameters. Answer: TRUE Diff: 1 Page Ref: 489 Main Heading: Types of Probability Key words: deterministic techniques 2) Probabilistic techniques assume that no uncertainty exists in model parameters. Answer: FALSE Diff: 1 Page Ref: 489 Main Heading: Types of Probability Key words: probabilistic techniques 3) Objective probabilities that can be stated prior to the occurrence of an event are classical or a priori. Answer: TRUE Diff: 2 Page Ref: 489 Main Heading: Types of Probability Key words: objective probabilities, classical probabilities 4) Objective probabilities that are stated after the outcomes of an event have been observed are relative frequencies. Answer: TRUE Diff: 2 Page Ref: 489 Main Heading: Types of Probability Key words: relative frequencies 5) Relative frequency is the more widely used definition of objective probability. Answer: TRUE Diff: 1 Page Ref: 490 Main Heading: Types of Probability Key words: relative frequencies 6) Subjective probability is an estimate based on personal belief, experience, or knowledge of a situation. Answer: TRUE Diff: 2 Page Ref: 490 Main Heading: Types of Probability Key words: subjective probability 7) An experiment is an activity that results in one of several possible outcomes. Answer: TRUE Diff: 1 Page Ref: 491 Main Heading: Fundamentals of Probability Key words: experiment 8) The events in an experiment are mutually exclusive if only one can occur at a time. Answer: TRUE Diff: 1 Page Ref: 491 Main Heading: Fundamentals of Probability Key words: mutually exclusive events 9) In a given experiment, the probabilities of all mutually exclusive events sum to one. Answer: TRUE Diff: 1 Page Ref: 491 Main Heading: Fundamentals of Probability Key words: mutually exclusive events, rules of probability 10) A set of events is collectively exhaustive when it includes all the events that can occur in an experiment. Answer: TRUE Diff: 2 Page Ref: 492 Main Heading: Fundamentals of Probability Key words: collectively exhaustive events 11) A marginal probability is the probability of a single event occurring. Answer: TRUE Diff: 1 Page Ref: 492 Main Heading: Fundamentals of Probability Key words: marginal probability 12) A Venn diagram visually displays mutually exclusive and nonmutually exclusive events. Answer: TRUE Diff: 2 Page Ref: 492 Main Heading: Fundamentals of Probability Key words: Venn diagram 13) A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously. Answer: FALSE Diff: 2 Page Ref: 493 Main Heading: Fundamentals of Probability Key words: joint probability 14) A conditional probability is the probability that an event occurs given that another event has already occurred. Answer: TRUE Diff: 1 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: conditional probability 15) Conditional probabilities are shown in Venn diagrams. Answer: FALSE Diff: 1 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: conditional probability 16) Probability trees are used only to compute conditional probabilities. Answer: FALSE Diff: 2 Page Ref: 496 Main Heading: Fundamentals of Probability Key words: probability tree, conditional probability 17) A succession of events that does not affect other events is independent. Answer: TRUE Diff: 1 Page Ref: 495 Main Heading: Statistical Independence and Dependence Key words: independence 18) A binomial probability distribution indicates the probability of r successes in n trials. Answer: TRUE Diff: 2 Page Ref: 497 Main Heading: Statistical Independence and Dependence Key words: binomial probability distribution 19) The chisquare test is a statistical test to determine if data that are squared exhibit bias. Answer: TRUE Diff: 1 Page Ref: 511 Main Heading: The Normal Distribution Key words: chisquare test 20) A continuous random variable may assume only integer values within a given interval. Answer: FALSE Diff: 1 Page Ref: 504 Main Heading: The Normal Distribution Key words: continuous random variables 21) Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed. Answer: FALSE Diff: 1 Page Ref: 504 Main Heading: The Normal Distribution Key words: normal distribution 22) Another name for the mean of a probability distribution is its expected value. Answer: TRUE Diff: 1 Page Ref: 503 Main Heading: Mean Key words: mean of probability distribution; expected value 23) An inspector correctly identifies defective products 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is 0.736. Answer: TRUE Diff: 2 Page Ref: 497 Main Heading: Statistical Independence and Dependence Key words: binomial probability distribution 24) In Bayesian analysis, additional information is used to alter the conditional probability of the occurrence of an event. Answer: FALSE Diff: 1 Page Ref: 495 Main Heading: Bayesian Analysis Key words: conditional probability 25) Objective probabilities that can be stated prior to the occurrence of an event are __________. Answer: classical or a priori Diff: 1 Page Ref: 489 Main Heading: Types of Probability Key words: probabilistic techniques, objective/classical probabilities 26) __________ probability is an estimate based on a personal belief, experience, and knowledge of a situation. Answer: Subjective Diff: 1 Page Ref: 490 Main Heading: Types of Probability Key words: subjective probability 27) The events in an experiment are __________ if only one can occur at a time. Answer: mutually exclusive Diff: 1 Page Ref: 491 Main Heading: Fundamentals of Probability Key words: mutually exclusive events 28) A __________ organizes numerical data to describe the events of an experiment. Answer: frequency distribution Diff: 1 Page Ref: 492 Main Heading: Fundamentals of Probability Key words: frequency distribution 29) A __________ is the probability of occurrence of a single event. Answer: marginal probability Diff: 1 Page Ref: 492 Main Heading: Fundamentals of Probability Key words: marginal probability 30) __________ can enable one to improve marginal probabilities of the occurrence of an event by gathering additional information. Answer: Bayesian analysis Diff: 2 Page Ref: 501 Main Heading: Fundamentals of Probability Key words: Bayesian analysis 31) A succession of events that do not affect each other are __________. Answer: independent Diff: 2 Page Ref: 495 Main Heading: Statistical Independence and Dependence Key words: independence 32) A __________ probability is the probability that an event will occur given that another event has already occurred. Answer: conditional Diff: 2 Page Ref: 495 Main Heading: Statistical Independence and Dependence Key words: conditional probability 33) In a binomial distribution process, there are __________ possible outcomes. Answer: two Diff: 2 Page Ref: 497 Main Heading: Statistical Independence and Dependence Key words: binomial distribution 34) One of the properties of the __________ distribution is that the probability of success remains constant over time. Answer: binomial Diff: 2 Page Ref: 497 Main Heading: Statistical Independence and Dependence Key words: binomial distribution 35) Altered marginal probability of an event based on additional information is a __________ probability. Answer: posterior Diff: 2 Page Ref: 501 Main Heading: Statistical Independence and Dependence Key words: Bayesian analysis, posterior probability 36) The __________ of a random variable is computed by multiplying each possible value of the variable by its probability and summing these products. Answer: expected value Diff: 1 Page Ref: 503 Main Heading: Statistical Independence and Dependence Key words: random variables, expected value 37) If events A and B are independent, then P(AB) = __________. Answer: P(A) ∙ P(B) Diff: 1 Page Ref: 495 Main Heading: Probability Key words: probabilistic techniques, objective/classical probabilities 38) If events A and B are independent, then P(AB) = __________. Answer: P(A) Diff: 1 Page Ref: 495 Main Heading: Probability Key words: probabilistic techniques, objective/classical probabilities 39) If two events are not mutually exclusive, then P(A or B) = __________. Answer: P(A) + P(B)  P(AB) Diff: 1 Page Ref: 495 Main Heading: Probability Key words: probabilistic techniques, objective/classical probabilities 40) __________ is a measure of dispersion of random variable values about the expected value. Answer: Variance Diff: 1 Page Ref: 503 Main Heading: Statistical Independence and Dependence Key words: random variables, variance 41) A continuous random variable can take on a(n) __________ number of values within a given interval. Answer: infinite Diff: 2 Page Ref: 504 Main Heading: The Normal Distribution Key words: continuous random variables 42) The __________ test is a statistical test to see if an observed data fit a particular probability distribution. Answer: chisquare Diff: 2 Page Ref: 511 Main Heading: The Normal Distribution Key words: chisquare test 43) The __________ normal distribution has a mean of 0 and a standard deviation of 1. Answer: standard Diff: 2 Page Ref: 504 Main Heading: The Normal Distribution Key words: standard normal distribution 44) Almost all of the data from a normal distribution fall within __________ standard deviations of the mean. Answer: 3 Diff: 1 Page Ref: 504 Main Heading: The Normal Distribution Key words: standard normal distribution 45) The expected value of the standard normal distribution is equal to __________. Answer: 0 Diff: 1 Page Ref: 504 Main Heading: The Normal Distribution Key words: expected value, standard normal distribution 46) The standard deviation of the standard normal distribution is equal to __________. Answer: 1 Diff: 1 Page Ref: 504 Main Heading: The Normal Distribution Key words: expected value, standard normal distribution Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. 47) What is the probability that Jim will be accepted at both universities? Answer: 0.09 Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: multiplication of probabilities 48) What is the probability that Jim will not be accepted at either university? Answer: 0.44 = (.55) x (.80) Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: multiplication of probabilities 49) What is the probability that Jim will be accepted by at least one of the two universities? Answer: 0.56 =1 [(.55) x (.80)] Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: multiplication of probabilities Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. Male (M) Female (F) Job Administrative (AD) 110 10 Salaried staff (SS) 30 50 Hourly staff (HS) 60 40 50) If an employee is selected at random, what is the probability that the employee is male? Answer: .667 = 200/300 Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: marginal probability 51) If an employee is selected at random, what is the probability that the employee is male and salaried staff? Answer: .10 = 30/300 Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: joint probability 52) If an employee is selected at random, what is the probability that the employee is female given that the employee is a salaried staff member? Answer: .625 = 50/80 Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: conditional probability 53) If an employee is selected at random, what is the probability that the employee is female or works as a member of the administration Answer: .70 = 100/300 + 120/300 10/300 Diff: 2 Page Ref: 495 Main Heading: Fundamentals of Probability Key words: not mutually exclusive events, addition rule An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable x_{i} represents the number of complaints, and p(x_{i}) is the probability of receiving x_{i} complaints.
54) What is the probability that they receive less than 3 complaints in a week? Answer: 0.43 Diff: 2 Page Ref: 492 Main Heading: Fundamentals of Probability Key words: probability distribution 55) What is the average number of complaints received per week? Answer: 2.83 Diff: 2 Page Ref: 503 Main Heading: Expected Value Key words: expected value, probability distribution 56) A fair die is rolled nine times. What is the probability that an odd number (1,3 or 5) will occur less than 3 times? Answer: 0.0899 Diff: 2 Page Ref: 495 Main Heading: The Binomial Distribution Key words: binomial distribution 57) A fair die is rolled 8 times. What is the probability that an even number (2,4, 6) will occur between 2 and 4 times? Answer: 0.6016 Diff: 2 Page Ref: 495 Main Heading: The Binomial Distribution Key words: binomial distribution A company markets educational software products, and is ready to place three new products on the market. Past experience has shown that for this particular software, the chance of "success" is 80%. Assume that the probability of success is independent for each product. 58) Find the probability that exactly 1 of the 3 products is successful. Answer: (3)(.8)(.2)(.2) = .096 Diff: 2 Page Ref: 497 Main Heading: The Binomial Distribution Key words: binomial distribution 59) Find the probability that none of the 3 products is successful. Answer: (1)(.2)(.2)(.2) = .008 Diff: 2 Page Ref: 497 Main Heading: The Binomial Distribution Key words: binomial distribution 60) If X has the following probability distribution X 1 2 3 4 P(X) .1 .5 .2 .2 Compute the expected value of X Answer: 2.5 EV = (1)(.1) + (2)(.5) + (3)(.2) + (4)(.2) =2.5 Diff: 2 Page Ref: 503 Main Heading: Expected Value Key words: expected value 61) If X has the following probability distribution X 1 2 3 4 P(X) .1 .5 .2 .2 Compute the standard deviation of X. Answer: .95524 Diff: 2 Page Ref: 503 Main Heading: Expected Value Key words: standard deviation 62) If x is normally distributed with a mean of 10 and a standard deviation of 3, then P(x ≤ 6) is equal to P( Z ≤ __)? Answer: 4/3 Diff: 3 Page Ref: 506 Main Heading: The Normal Distribution Key words: normal distribution 63) For a standard normal distribution, what is the probability that z is greater than 1.75? Answer: 0.0401 Diff: 3 Page Ref: 506 Main Heading: The Normal Distribution Key words: normal distribution Two Psychology majors, in 2 different sections of Clinical Psychology, were comparing test scores. The following gives the students' scores, class mean, and standard deviation for each section: Section 1 Section 2 Student Score 84 75 Mean 75 60 Standard deviation 7 8 64) What is the zscore of the student from section 1 and what is the probability that a student in section 1 will score higher than 84? Answer: 1.286 and .0985 Diff: 3 Page Ref: 506509 Main Heading: The Normal Distribution Key words: normal distribution 65) What is the zscore of the student from section 2 and what is the probability that a student in section 2 will score higher than 75? Answer: 1.875 and .0301 Diff: 3 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 66) Which student scored better compared to the rest of the section? Answer: section 2 student because their zscore is higher Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: mean, standard deviation 67) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz? Answer: 0.9772 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 68) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf of bread is larger than 23 oz? Answer: 0.0228 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 69) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is less than 24 oz? Answer: 1 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 70) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 20.75 and 23.25 oz? Answer: 0.9876 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 71) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is between 21.75 and 22.25 oz? Answer: 0.3830 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 72) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz? Answer: 0 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 73) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 22.25 oz? Answer: 0.3085 Diff: 2 Page Ref: 506509 Main Heading: The Normal Distribution Key words: norm distrib, probability calculations with normal distribution 74) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive payments beyond age 75? Answer: 0.0401 Diff: 1 Page Ref: 506509 Main Heading: Normal Distribution, Probability Key words: norm distrib, probability calculations with normal distribution 75) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. What proportion of the participants die before they reach the age of 65? Answer: 0.2266 Diff: 2 Page Ref: 506509 Main Heading: Normal Distribution, Probability Key words: norm distrib, probability calculations with normal distribution 76) A life insurance company wants to estimate their annual payouts. Assume that the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 4 years. By what age have 80% of the plan participants pass away? Answer: 71.36 years old Diff: 3 Page Ref: 506509 Main Heading: Normal Distribution, Value Key words: norm distrib, probability calculations with normal distribution 77) For the normal distribution, the mean plus and minus 1.96 standard deviations will include what percent of the observations? Answer: 95% Diff: 1 Page Ref: 506509 Main Heading: The Normal Distribution Key words: normal distribution 78) What is the area under the normal curve for ≥ 1.79? Answer: 0.0367 Diff: 3 Page Ref: 506509 Main Heading: The Normal Distribution Key words: normal distribution 79) A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equaled 5 days. Assuming that the distribution is normal, what percent of the invoices is paid within 15 days of receipt? Answer: 15.87% Diff: 3 Page Ref: 506509 Main Heading: The Normal Distribution Key words: normal distribution 80) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of the crab are normally distributed, what is the probability that a randomly selected crab will weigh more than 2 .2 pounds? Answer: 0.0668 Diff: 1 Page Ref: 506509 Main Heading: Normal Distribution, Probability Key words: norm distrib, probability calculations with normal distribution 81) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crab are normally distributed, what is the probability that a randomly selected crab will weigh between 1 and 2 pounds? Answer: 0.7745 Diff: 1 Page Ref: 506509 Main Heading: Normal Distribution, Probability Key words: norm distrib, probability calculations with normal distribution 82) The owner of a seafood market determined that the average weight for a crab is 1.6 pounds with a standard deviation of 0.4 pound. Assuming the weights of crab are normally distributed, the probability that a randomly selected crab will weigh less than 1.2 pounds is __________. Answer: 0.1587 Diff: 1 Page Ref: 506509 Main Heading: Normal Distribution, Probability Key words: norm distrib, probability calculations with normal distribution 83) Assume that 