Review Exercises 289 57. The mean ACT composite score in a recent year is 20.7. A random sample of 36 ACT composite scores is selected. What is the probability that the mean score for the sample is (a) less than 22, (b) greater than 23, and (c) between 20 and 21.5? Assume s = 5.9. (Source: ACT, Inc) 58. The mean MCAT total score in a recent year is 500.9. A random sample of 32 MCAT total scores is selected. What is the probability that the mean score for the sample is (a) less than 503, (b) more than 502, and (c) between 498 and 501? Assume s = 10.6. (Source: Association of American Medical Colleges) 59. The mean annual salary for Level 1 actuaries in the United States is about $72,000. A random sample of 45 Level 1 actuaries is selected. What is the probability that the mean annual salary of the sample is (a) less than $75,000 and (b) more than $68,000? Assume s = $11,000. (Adapted from Salary.com) 60. The mean annual salary for physical therapists in the United States is about $87,000. A random sample of 50 physical therapists is selected. What is the probability that the mean annual salary of the sample is (a) less than $84,000 and (b) more than $85,000? Assume s = $10,500. (Adapted from Salary.com) Section 5.5 In Exercises 61 and 62, a binomial experiment is given. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. 61. A survey of U.S. adults ages 33 to 40 earning more than $150,000 per year found that 94% are content with how their lives have turned out so far. You randomly select 20 U.S. adults ages 33 to 40 earning more than $150,000 and ask if they are content with their lives so far. (Source: The Harris Poll) 62. A survey of U.S. adults found that 69% have a favorable view of farming and agriculture. You randomly select 45 U.S. adults and ask whether they have a favorable view of farming and agriculture. (Source: Gallup) In Exercises 63–68, write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. 63. P1x Ú 252 64. P1x … 362 65. P1x = 452 66. P1x 7 142 67. P1x 6 602 68. P154 6 x 6 642 In Exercises 69 and 70, determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distribution to find the indicated probabilities. 69. A survey of U.S. adults found that 72% used a mobile device to manage their bank account at least once in the previous month. You randomly select 70 U.S. adults and ask whether they used a mobile device to manage their bank account at least once in the previous month. Find the probability that the number who have done so is (a) at most 40, (b) exactly 50, and (c) greater than 60. (Source: American Bankers Association) 70. Thirty-four percent of U.S. college graduates work in jobs that do not require a college degree. You randomly select 20 U.S. college graduates. Find the probability that the number working in a job that does not require a college degree is (a) exactly 7, (b) at most 6, and (c) between 5 and 10, inclusive. Identify any unusual events. (Source: Inside Higher Ed)
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