282 CHAPTER 5 Normal Probability Distributions Approximating Binomial Probabilities In Exercises 19–26, 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. Identify any unusual events. Explain. 19. College Programs In a survey of U.S. college students, 62% said that if their college offers new programs tailored to the new economy, it will make them more likely to re-enroll. You randomly select 40 college students. Find the probability that the number who are more likely to enroll if their college offers new programs tailored to the new economy is (a) exactly 25, (b) at least 30, and (c) at most 24. (Source: New America) 20. Social Media A survey of Americans found that 55% would be disappointed if Facebook disappeared. You randomly select 500 Americans and ask them whether they would be disappointed if Facebook disappeared. Find the probability that the number who say yes is (a) less than 250, (b) at least 300, and (c) between 240 and 280, inclusive. (Source: The Verge) 21. Gun Legislation In a survey of U.S. adults, 43% said they would favor allowing people to carry guns in more places. You randomly select 100 U.S. adults. Find the probability that the number who favor allowing people to carry guns in more places is (a) more than 50, (b) at most 50, and (c) between 40 and 45, inclusive. (Source: Pew Research Center) 22. Perception of Police A survey of U.S. registered voters found that 71% have a favorable opinion of police. You randomly select 150 U.S. registered voters. Find the probability that the number who have a favorable opinion of police is (a) at most 100, (b) more than 120, and (c) between 90 and 110, inclusive. (Source: Harvard CAPS/Harris Poll) 23. Athletes on Social Issues In a survey of college athletes, 84% said they are willing to speak up and be more active in social issues. You randomly select 25 college athletes. Find the probability that the number who are willing to speak up and be more active in social issues is (a) at least 24, (b) less than 23, and (c) between 18 and 22, inclusive. (Source: Rise) 24. Gun Ownership In a survey of U.S. registered voters, 36% said that someone in their household owns a gun. You randomly select 20 U.S. registered voters. Find the probability that the number who live with someone who owns a gun is (a) no more than 8, (b) exactly 7, and (c) between 6 and 9 inclusive. (Source: Harvard CAPS/Harris Poll) 25. Clinical Trials In a survey of U.S. adults, 19% said that they have participated in a clinical trial. You randomly select 200 U.S. adults. Find the probability that the number who have participated in a clinical trial is (a) no fewer than 30, (b) more than 40, and (c) between 35 and 45 inclusive. (Source: America Speaks!) 26. Advancing Research In a survey of U.S. adults, 77% said are willing to share their personal health information to advance medical research. You randomly select 500 U.S. adults. Find the probability that the number who are willing to share their personal health information to advance medical research is (a) at most 400, (b) more than 360, and (c) between 380 and 390 inclusive. (Source: America Speaks!)
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