SECTION 5.5 Normal Approximations to Binomial Distributions 283 27. Daily Commute About 83% of U.S. employees drive their own vehicle to work. You randomly select a sample of U.S. employees. Find the probability that more than 100 of the employees drive their own vehicle to work. (Source: U.S. Bureau of Labor Statistics) (a) You select 110 U.S. employees. (b) You select 125 U.S. employees. (c) You select 150 U.S. employees. 28. Employee Wellness A survey of employed U.S. adults found that only 35% believe their employer cares about their well-being. You randomly select a sample of U.S. employees. Find the probability that fewer than 100 believe their employer cares about their well-being. (Source: Gallup) (a) You select 250 U.S. employees. (b) You select 300 U.S. employees. (c) You select 400 U.S. employees. Extending Concepts Getting Physical The figure shows the results of a survey of U.S. adults ages 18 to 29 who were asked whether they participated in a sport. In the survey, 48% of the men and 23% of the women said they participate in sports. The most common sports are shown below. Use this information in Exercises 29 and 30. (Source: NPR) 22% 22% 13% 6% 5% Basketball Soccer Football Baseball/Softball Running/Track Participation Rates by Sport Men 16% 13% 12% 11% 9% Baseball/Softball Volleyball Running/Track Tennis Basketball Women 29. You randomly select 250 U.S. men ages 18 to 29 and ask them whether they participate in at least one sport. You find that 80% say no. How likely is this result? Do you think this sample is a good one? Explain your reasoning. 30. You randomly select 300 U.S. women ages 18 to 29 and ask them whether they participate in at least one sport. Of the 72 who say yes, 50% say they participate in volleyball. How likely is this result? Do you think this sample is a good one? Explain your reasoning. Testing a Drug A drug manufacturer claims that a drug cures a rare skin disease 75% of the time. The claim is checked by testing the drug on 100 patients. If at least 70 patients are cured, then this claim will be accepted. Use this information in Exercises 31 and 32. 31. Find the probability that the claim will be rejected, assuming that the manufacturer’s claim is true. 32. Find the probability that the claim will be accepted, assuming that the actual probability that the drug cures the skin disease is 65%.
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