Exercise Set 7.4: The Binomial Distribution Determine if each of the experiments below is a binomial experiment. (Answer Yes or No.) If the answer is No, explain which requirement(s) have not been met. 1. A fair die is tossed 5 times to determine the number of times that an odd number is obtained. 2. A fair die is rolled until a \"2\" is obtained. 3. A fair die is tossed 8 times, noting the uppermost number of each toss. 4. A fair die is tossed 10 times to determine the number of times that \"a roll is greater than 1\". 5. The following fair spinner is spun until a \"4\" is obtained\". 1 2 3 5 4 6. The following fair spinner is spun 10 times to determine the number of times that a \"3\" is obtained. 1 2 3 A jar contains 8 blue marbles, 10 green marbles and 12 yellow marbles. Determine if each of the experiments below is a binomial experiment. (Answer Yes or No.) If the answer is No, explain which requirement(s) of a binomial experiment have not been met. 7. Four marbles are drawn in succession and with replacement, noting each time whether or not the marble is blue. 8. Five marbles are drawn in succession and without replacement, noting each time whether or not the marble is yellow. 9. Marbles are drawn in succession and with replacement until a green marble is obtained. MATH 1313 Finite Mathematics with Applications 10. Six marbles are drawn in succession and with replacement, noting the color of the marble on each draw. 11. Seven marbles are drawn in succession and without replacement, noting each time whether or not the marble is green. 12. Eight marbles are drawn in succession and with replacement, noting each time whether or not the marble is blue. An experiment consists of 8 independent trials where the probability of success on each trial is 83 . Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. Exactly 3 successes. Exactly 6 successes. Exactly 1 success. Exactly 5 successes. At least 1 success. At least 2 successes. At least 6 successes. At least 7 successes. At most 7 successes. At most 6 successes. At most 2 successes. At most 1 success. No successes. All successes. A biased coin is tossed 10 times and the probability of obtaining heads is 0.6. Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 27. 28. 29. 30. 31. 32. 33. Exactly 8 heads. Exactly 6 heads. Exactly 3 heads. Exactly 9 heads. At least 2 heads. At least 1 heads. At least 8 heads. 489 Exercise Set 7.4: The Binomial Distribution 34. 35. 36. 37. 38. 39. 40. 62. An experiment consists of tossing a biased coin 11 times and observing the number of times the coin lands on heads. The probability that the coin lands on heads is 0.75 . At least 9 heads. At most 9 heads. At most 8 heads. At most 1 head. At most 2 heads. All heads. No heads. Suppose that X is the number of successes in an experiment with 9 independent trials where the probability of success is 52 . Find each of the following probabilities. Round answers to the nearest ten-thousandth. 41. P ( X = 2 ) 50. P ( X > 6 ) 42. P ( X = 4 ) 51. P ( X 1) 43. P ( X = 0 ) 52. P ( X 2 ) 44. P ( X = 9 ) 53. P ( 2 < X < 6) 45. P ( X < 3) 54. P (1 < X < 4 ) 46. P ( X < 2 ) 55. P ( 3 X 6) 47. P ( X 7 ) 56. P (1 X 5) 48. P ( X 6 ) 57. P ( 0 X < 4 ) 49. P ( X > 8 ) 58. P ( 6 < X 9 ) For each binomial experiment described in problems 59-68, find: A. The mean. B. The variance. C. The standard deviation. Round answers to the nearest tenthousandth. 59. An experiment consists of tossing a fair coin 8 times and observing the number of times the coin lands on heads. 60. An experiment consists of tossing a fair coin 12 times and observing the number of times the coin lands on tails. 61. An experiment consists of tossing a biased coin 15 times and observing the number of times the coin lands on heads. The probability of landing on heads is 0.66 . 490 63. An experiment consists of tossing a biased coin 16 times and observing the number of times the coin lands on heads. The probability that the coin lands on tails is 0.40 . 64. An experiment consists of tossing a biased coin 13 times and observing the number of times the coin lands on heads. The probability that the coin lands on tails is 0.35 . 65. Fifty college students are tested to see if they have a specific food allergy. The probability that a randomly selected person has the food allergy is 0.082. 66. Sixty college students are tested to see if they have a specific food allergy. The probability that a randomly selected person has the food allergy is 0.065. 67. The probability that a restaurant passes its health department inspection is 0.96. The owners of 46 restaurants are surveyed to see if their restaurants passed inspection. 68. The probability that a restaurant passes its health department inspection is 0.94. The owners of 58 restaurants are surveyed to see if their restaurants passed inspection. Answer the following. 69. The probability that a tire will wear out before its warranty expires is 0.29. If The Tire Store sells 28 tires in one afternoon, what is the probability that exactly 8 tires will wear out before the warranty expires? 70. The probability that a tire will wear out before its warranty expires is 0.21. If The Tire Store sells 36 tires in one afternoon, what is the probability that exactly 11 tires will wear out before the warranty expires? University of Houston Department of Mathematics Exercise Set 7.4: The Binomial Distribution 71. The probability that a tire will wear out before its warranty expires is 0.27. If The Tire Store sells 16 tires in one afternoon, what is the probability that at most 2 tires will wear out before the warranty expires? 80. A hospital purchases thermometers in lots of 1000. On the average, 3 out of every lot are defective. If 10 thermometers are selected from one lot, what is the probability that none of them are defective? 72. The probability that a tire will wear out before its warranty expires is 0.24. If The Tire Store sells 20 tires in one afternoon, what is the probability that at most 3 tires will wear out before the warranty expires? 81. A hospital purchases thermometers in lots of 1000. On the average, 4 out of every lot are defective. If 12 thermometers are selected from one lot, what is the probability that at least 1 of them is defective? 73. The probability that a tire will wear out before its warranty expires is 0.26. If The Tire Store sells 24 tires in one afternoon, what is the probability that at least 2 tires will wear out before the warranty expires? 74. The probability that a tire will wear out before its warranty expires is 0.28. If The Tire Store sells 12 tires in one afternoon, what is the probability that at least 1 tire will wear out before the warranty expires? 75. The probability that a marksman will hit a target each time he shoots is 0.88. If he fires 12 times, what is the probability that he hits the target exactly 9 times? 76. The probability that a marksman will hit a target each time he shoots is 0.82. If he fires 14 times, what is the probability that he hits the target exactly 11 times? 82. A hospital purchases thermometers in lots of 1000. On the average, 1 out of every lot is defective. If 14 thermometers are selected from one lot, what is the probability that at least 2 of them are defective? 83. A hospital purchases thermometers in lots of 1000. On the average, 5 out of every lot are defective. If 16 thermometers are selected from one lot, what is the probability that at most 2 of them are defective? 84. A hospital purchases thermometers in lots of 1000. On the average, 3 out of every lot are defective. If 12 thermometers are selected from one lot, what is the probability that at most 1 of them is defective? 77. The probability that a marksman will hit a target each time he shoots is 0.85. If he fires 10 times, what is the probability that he hits the target at most 8 times? 78. The probability that a marksman will hit a target each time he shoots is 0.89. If he fires 15 times, what is the probability that he hits the target at most 13 times? 79. A hospital purchases thermometers in lots of 1000. On the average, 2 out of every lot are defective. If 15 thermometers are selected from one lot, what is the probability that none of them are defective? MATH 1313 Finite Mathematics with Applications 491 Math 1313 Homework 26 Section 7.4 1. The choices for the problem number 16 from the book are given below. a. 0.0304 b. 0.1014 c. 0.6250 d. 0.3819 e. 0.0472 2. The choices for problem number 20 from the book are given below. a. 0.0056 b. 0.1313 c. 0.8650 d. 0.2614 e. 0.0311 3. The choices for problem number 24 from the book are given below. a. 0.8650 b. 0.9944 c. 0.0506 d. 0.7480 e. 0.1350 4. The choices for problem number 32 from the book are given below. a. 0.0432 b. 0.6817 c. 0.9999 d. 0.0464 e. 0.8742 5. The choices for problem number 38 from the book are given below. a. 0.9103 b. 0.8658 c. 0.1301 d. 0.4578 e. 0.0123 6. The choices for problem number 50 from the book are given below. a. 0.1032 b. 0.9295 c. 0.0250 d. 0.8491 e. 0.0003 7. The choices for problem number 58 from the book are given below. a. 0.0250 b. 0.9295 c. 0.8691 1 Math 1313 Homework 26 Section 7.4 d. 0.5712 e. 0.0123 8. The choices for problem number 62 part a from the book are given below. a. 8.25 b. 54.52 c. 825 d. 2.75 e. 4.125 9. The choices for problem 66 part b from the book are given below. a. 3.9801 b. 3.2712 c. 3.3288 d. 3.6465 e. 5.4506 10. The choices for problem number 78 from the book are given below. a. 0.4969 b. 0.9089 c. 0.5031 d. 0.2793 e. 0.7207 2 TMobile LTE 11:08 PM Math 1313 Homework 26 Section 7.4 l. The choices for the problem number 16 from the book are given below. a. 0.0304 0.1014 0.6250 0.3819 0.0472 Pia-P.0- 2. The choices for problem number 20 from the book are given below. 0.0056 0.1313 0.8650 0.2614 0.031] {FF-PET?\" 3. The choices for problem number 24 from the book are given below. a. 0.3650 0.9944 0.0506 0.?480 0. 1350 Fla-PW 4. The choices for problem number 32 from the book are given below. 0.0432 0.681:Ir 0.9999 0.0464 0.3742 951.0531\" 5. The choices for problem number 38 from the book are given below. 0.9103 0.3658 0.1301 0.4578 0.0123 9219ch 6. The choices for problem number 50 from the book are given below. 0.1032 0.9295 0.0250 0.349] 0.0003 {PP-PET?\" ?. The choices for problem number 58 from the book are given below. a. 0.0250 b. 0.9295 c. 0.869] Math 1313 Homework 26 Section 7.4 d. 05312 e. 0.0123 . The choices for problem number 62 part a from the book are given below. a. 8.25 b. 54.52 c. 825 d. 2.75 e. 4.125 . The choices for problem 66 part b from the book are given below. a. 3.9801 b. 3.2712 :3. 3.3233 [1. 3.6465 6. 5.4506 0. The choices for problem number 78 from the book are given below. a. 0.4969 b. 0.9089 0.503] 0.2?93 0. 720'? an F\" TMobile LTE 11:08 PM Math 1313 Homework 26 Section 7.4 l. The choices for the problem number 16 from the book are given below. a. 0.0304 0.1014 0.6250 0.3819 0.0472 Pia-P.0- 2. The choices for problem number 20 from the book are given below. 0.0056 0.1313 0.8650 0.2614 0.031] {FF-PET?\" 3. The choices for problem number 24 from the book are given below. a. 0.3650 0.9944 0.0506 0.?480 0. 1350 Fla-PW 4. The choices for problem number 32 from the book are given below. 0.0432 0.681:Ir 0.9999 0.0464 0.3742 951.0531\" 5. The choices for problem number 38 from the book are given below. 0.9103 0.3658 0.1301 0.4578 0.0123 9219ch 6. The choices for problem number 50 from the book are given below. 0.1032 0.9295 0.0250 0.349] 0.0003 {PP-PET?\" ?. The choices for problem number 58 from the book are given below. a. 0.0250 b. 0.9295 c. 0.869] Math 1313 Homework 26 Section 7.4 d. 05312 e. 0.0123 . The choices for problem number 62 part a from the book are given below. a. 8.25 b. 54.52 c. 825 d. 2.75 e. 4.125 . The choices for problem 66 part b from the book are given below. a. 3.9801 b. 3.2712 :3. 3.3233 [1. 3.6465 6. 5.4506 0. The choices for problem number 78 from the book are given below. a. 0.4969 b. 0.9089 0.503] 0.2?93 0. 720'? an F\