Review Exercises 227 In Exercises 19 and 20, find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results and determine any unusual values. 19. About 13% of U.S. drivers are uninsured. You randomly select eight U.S. drivers and ask them whether they are uninsured. The random variable represents the number who are uninsured. (Source: Insurance Research Council) 20. Thirty-three percent of NCAA student-athletes have a job waiting for them when they graduate college. You randomly select ten NCAA student-athletes who are graduating and ask them whether they have a job waiting for them. The random variable represents the number who have a job waiting for them. (Source: Gallup) Section 4.3 In Exercises 21–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. 21. Fourteen percent of noninstitutionalized U.S. adults smoke cigarettes. After randomly selecting ten noninstitutionalized U.S. adults, you ask them whether they smoke cigarettes. Find the probability that the first adult who smokes cigarettes is (a) the third person selected, (b) the fourth or fifth person selected, and (c) not one of the first six persons selected. (Source: National Center for Health Statistics) 22. From 1940 to 2020, tornadoes killed about 0.26 people per day in the United States. Assume this rate holds true today and is constant throughout the year. Find the probability that the number of people in the United States killed by a tornado tomorrow is (a) exactly zero, (b) at most two, and (c) more than one. (Source: National Weather Service) 23. Thirty-six percent of Americans think there is still a need for the practice of changing their clocks for Daylight Savings Time. You randomly select seven Americans. Find the probability that the number who say there is still a need for changing their clocks for Daylight Savings Time is (a) exactly four, (b) less than two, and (c) at least six. (Source: Rasmussen Reports) 24. In a recent season, hockey player Evgeni Malkin scored 25 goals in 55 games he played. Assume that his goal production stayed at that level for the next season. Find the probability that he would get his first goal (a) in the first game of the season, (b) in the second game of the season, (c) within the first three games of the season, and (d) not within the first three games of the season. (Source: National Hockey League) 25. During a 10-year period, sharks killed an average of 6.4 people each year worldwide. Find the probability that the number of people killed by sharks next year is (a) exactly three, (b) more than six, and (c) at most five. (Source: International Shark Attack File) 26. Sixty-nine percent of U.S. adults plan to get a COVID-19 vaccine or already have. You randomly select ten U.S. adults and ask them whether they plan to get a COVID-19 vaccine or already have. Find the probability that the number who plan to get a COVID-19 vaccine or already have is (a) exactly seven, (b) more than eight, and (c) from two to four. (Source: Pew Research)
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