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Chapter 5 - Discrete Probability Distributions 1. _________ ________ _________ are obtained from data that can be measured rather than counted. 3. The sum of the probabilities of all the events in the sample space of a probability distribution must equal to ______ 4. A(n) __________ variable is one in which values are determined by chance. 5. A(n) __________ probability distribution consists of the finite number of values a random variable can assume and the corresponding probabilities of the values. 6. The following distribution is not a probability distribution because X 2 1 0 1 2 P(X) 0.16 0.26 0.40 0.12 0.27 7. The following distribution is not a probability distribution because X 2 1 0 1 2 P(X) 0.18 0.19 –0.16 0.55 0.24 8. For the following data, construct a graph showing the probability distribution. X 0 1 2 3 4 P(X) 0.35 0.25 0.20 0.15 0.05 9. The number of song requests a radio station receives per day is indicated in the table below. Construct a graph for this data. Number of calls X 8 9 10 11 12 Probability P(X) 0.21 0.31 0.16 0.14 0.18 10. The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph. 11. Construct the probability distribution for the number of heads obtained when tossing four coins. Draw a graph of the distribution. 12. Find the mean of the distribution shown. X 1 2 P(X) 0.27 0.73 13. Give the variance of the following distribution? X 0 1 2 3 4 P(X) 0.20 0.35 0.10 0.25 0.10 14. Find the mean of the distribution shown below. X 2 3 4 P(X) 0.28 0.40 0.32 A 15. Find the mean of the distribution shown. X 4 6 P(X) 0.28 0.72 16. What is the standard deviation of the following probability distribution? X 0 2 4 6 8 P(X) 0.20 0.05 0.35 0.25 0.15 17. Find the mean of the distribution shown below. X 4 2 0 2 P(X) 0.35 0.24 0.31 0.10 18. Give the mean of the following probability distribution? X 2 3 4 5 P(X) 0.50 0.25 0.15 0.10 19. Find the mean of the distribution shown. X 3 2 1 0 P(X) 0.19 0.24 0.53 0.04 20. The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. Number of cartoons watched X 0 1 2 3 4 5 Probability P(X) 0.15 0.20 0.30 0.10 0.20 0.05 What is the mean of the data? 21. The number of cartoons watched on Saturday mornings by students in Mrs. Kelly's first grade class is shown below. Number of cartoons watched X 0 1 2 3 4 5 Probability P(X) 0.15 0.20 0.30 0.10 0.20 0.05 Give the standard deviation for the probability distribution. 22. Using the probability distribution listed, the mean would be ______. X 0 1 2 3 P(X) 0.2 0.1 0.3 0.4 23. Find the mean of the distribution shown below. X 2 3 4 P(X) 0.28 0.24 0.48 24. If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game? 25. The formula for the variance of a probability distribution is __________. 31. In a large bag of marbles, 40% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles? 32. A coin is tossed five times. Find the probability of getting exactly three heads. 33. If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices. 34. A pet supplier has a stock of parakeets of which 30% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet? 35. A jewelry supplier has a supply of earrings which are 40% platinum. A store owner orders five sets of earrings from the supplier. If the supplier selects the pairs of earrings at random, what is the chance that the jewelry store gets exactly two sets of platinum pairs? 36. If 1.5% of the bolts made by an automotive factory are defective, what is the probability that in a shipment of 200 bolts, there are 6 defective bolts? 37. A student takes a 7 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 3 questions correct? 38. A computer store has 75 printers of which 20 are laser printers and 55 are ink jet printers. If a group of 10 printers is chosen at random from the store, find the mean and variance of the number of ink jet printers. 39. A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed. 40. A multiple choice quiz consists of 20 questions, each with 4 possible answers. Find the mean for the number of correct answers, if a student guesses on each question. 41. A die is rolled 360 times. Find the standard deviation of the number of times a 3 will be rolled. 42. In a survey, 65% of the voters support a particular referendum. If 10 voters are chosen at random, find the standard deviation of the number of voters who support the referendum. 43. A certain large manufacturing facility produces 20,000 parts each week. The manager of the facility estimates that about 1% of the parts they make are defective. What is the variance for the number of defective parts made each week? 44. A university has 10,000 students of which 45% are male and 55% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students. 45. The failure rate for taking the bar exam in Philadelphia is 41%. If 375 people take the bar exam, what is the mean for the number of failures? 46. A school is sending 18 children to a camp. If 15% of the children in the school are first graders, and the 18 children are selected at random from among all 6 grades at the school, find the mean and variance of the number of first graders chosen? 47. In a survey, 65% of the voters support a particular referendum. If 30 voters are chosen at random, find the mean and variance for the number of voters who support the referendum. 48. Use the multinomial formula and find the probability for the following data. n 6, X1 3, X 2 2, X 3 1, p1 0.58, p2 0.25, p3 0.17 49. Use the multinomial formula and find the probability for the following data. n 8, X1 4, X 2 3, X 3 1, p1 0.30, p2 0.50, p3 0.20 50. Use the multinomial formula to find the probability for the following situation. X1 = 1, X2 = 2, X3 = 3 when n = 6, p1 = 0.4, p2 = 0.5, p3 = 0.1 51. Use the multinomial formula to find the probability for the situation in which n = 6, X1 = 2, X2 = 2, X3 = 2, and, p1 = 0.4, p2 = 0.4, p3 = 0.2. 52. The probability that federal income tax returns will have 0, 1, or 2 errors is 0.73, 0.23, and 0.04, respectively. If 10 randomly selected returns are audited, what is the probability that eight will have no errors, two will have one error, and none will have two errors? 53. On a Saturday evening in Chicago, 34% of the people go out to dinner, 18% go out to see a movie, 13% go out to a party, and 35% stay home. If five people are randomly selected on Monday morning, what is the probability that all but one went out Saturday night? 54. The probability that a person will have 0, 1, or 2 dental checkups per year is 0.3, 0.6, and 0.1, respectively. If seven people are picked at random, what is the probability that two will have no checkups, four will have one checkup, and one will have two checkups in the next year? 55. The probability that a Poisson random variable X is equal to 2, where = 7, is 56. A certain type of battery has a 0.5% failure rate. Find the probability that a shipment of 1,000 batteries has more than two defective batteries. 57. If there are 20 typographical errors randomly distributed in a 250-page document, find the probability that a given page contains exactly two errors. 58. In the instructor's answer book for a mathematics text, 10% of the answers are incorrect. Use the Poisson approximation to express the probability that there are exactly 2 incorrect answers for a homework set with 50 problems. 59. A bag contains 20 white marbles and 40 black marbles. If 9 marbles are chosen, what is the probability that there will be 4 white marbles and 5 black marbles? 60. A survey of 13 people at a bookstore showed that five had purchased a hardcover book. If seven people are selected at random, what is the probability that four of them had purchased a hardcover book? 61. A school club consists of 24 male students and 15 female students. If 4 students are selected to represent the club in the student government, what is the probability 2 will be male and 2 will be female? Group 2 Test Item File to accompany Elementary Statistics: A Step by Step Approach 5th edition Chapter 5: Discrete Probability Distributions 1. What value would be needed to complete the following probability distribution? x P( x) 0 1/3 1 1/8 2 1/8 3 4 1/6 2. Give the mean of the following probability distribution? x P( x) 1 0.20 2 0.10 3 0.35 4 0.05 5 0.30 Use the following to answer questions 3-4: The number of cartoons watched by Mrs. Kelly's first grade class on Saturday morning is shown below. x P( x) 0 0.15 1 0.20 2 0.30 3 0.10 4 0.20 5 0.05 3. What is the mean distribution of the data given above? 4. Give the standard deviation for the probability distribution above. 5. Give the variance of the following distribution? x P( x) 0 0.20 1 0.35 2 0.10 3 0.25 4 0.10 6. What is the standard deviation of the following probability distribution? x P( x) 0 0.20 2 0.05 4 0.35 6 0.25 8 0.15 7. If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expectation of this game? 8. A coin is tossed five times. Find the probability of getting exactly three heads. 9. If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices. 10. A die is rolled 360 times. Find the standard deviation for the number of 3s that will be rolled. 11. The foreman at a large plant estimates that there are defective parts about 1% of the time. If the plant produces 20,000 parts in a week, what is the variance for the number of defective parts? 12. The failure rate for taking the bar exam in Philadelphia is 41%. If 375 people take the bar exam, what is the mean for the number of failures? 13. A coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed. 14. Using the multinomial formula, find the probability of the following data. n 17, x1 8, x2 5, x3 4 p1 0.58, p2 0.25, p3 017 . 15. Using the multinomial formula, find the probability of the following data. n 8, x1 4, x2 3, x3 1 p1 0.3, p2 0.5, p3 0.2 16. A survey of 12 people at a bookstore showed that five had purchased a hardcover book. If seven people are selected at random, what is the probability that four of them had purchased a hardcover book? 17. The probability that federal income tax returns will have 0, 1, or 2 errors is 0.53, 0.15, and 0.32, respectively. If 10 randomly selected returns are audited, what is the probability that six will have no errors, three will have one error, and one will have two errors? 18. The probability that a person will have 0, 1, or 2 dental checkups per year is 0.2, 0.5, and 0.3, respectively. If seven people are picked at random, what is the probability that two will have no checkups, four will have one checkup, and one will have two checkups in the next year? 19. On a Saturday evening, 34% of the people in Chicago go out to dinner, 18% see a movie, 13% have a party, and 35% stay home. If seven people are randomly selected, what is the probability that one eats out, three see a movie, two have a party, and one stays at home? 20. A package of 10 batteries is checked to determine if there are any dead batteries. Four batteries are checked. If one or more are dead, the package is not sold. What is the probability that the package will not be sold if there are actually three dead batteries in the package? 26. If the standard deviation of a probability distribution is 1.71, the variance is _____. 27. The probability of a success must remain the same for each trial in a _______ experiment. 28. In binomial experiments, the outcomes are usually classified as _________or _______. 29. In a binomial experiment, the outcomes of each trial must be _________ on each other. 30. The outcomes of a binomial experiment and the corresponding probabilities of these outcomes are called a binomial ____________. 36. A(n) __________ is one in which values are determined by chance. 37. A(n) __________ probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. 38. The __________ of a discrete random variable of a probability distribution is the theoretical average of the variable. 39. The formula for the variance of a probability distribution is __________. 40. The symbol __________ is used for the expected value. 41. One of the requirements for a binomial experiment is that there must be a __________ number of trials. 42. If a trial in an experiment has more than two outcomes, a(n) __________ distribution must be used. 44. Draw a graph showing the probability distribution for the sample space for tossing four coins. 45. For the following data, construct a graph showing the probability distribution. x bg P x 0 0.35 1 0.25 2 0.20 3 0.15 4 0.05 46. The figure below represents the probability distribution for selecting a number of objects out of a container. Construct a probability distribution from this graph. 47. The number of song requests a radio station receives per day is indicated in the table below. Construct a graph for this data. Number of calls, x 8 9 10 11 12 Probability, P x bg 0.21 0.31 0.16 0.14 0.18 48. If 1.5% of the bolts made by an automotive factory are defective, what is the probability that in a shipment of 200 bolts, there are 6 defective bolts?