212 CHAPTER 4 Discrete Probability Distributions Constructing and Graphing Binomial Distributions In Exercises 27–30, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. 27. College Acceptance Pennsylvania State University accepts 49% of applicants. You randomly select seven Pennsylvania State University applicants. The random variable represents the number who are accepted. (Source: US News & World Report) 28. Immigration Thirty-three percent of immigrants to the United States ages 25 and older have a bachelor’s degree or higher. You randomly select eight immigrants to the U.S. ages 25 and older. The random variable represents the number who have a bachelor’s degree or higher. (Source: Migration Policy Institute) 29. Living to Age 100 Seventy-seven percent of adults want to live to age 100. You randomly select five adults and ask them whether they want to live to age 100. The random variable represents the number who want to live to age 100. (Source: Standford Center on Longevity) 30. Workplace Cleanliness Fifty-seven percent of employees judge their peers by the cleanliness of their workspaces. You randomly select 10 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number who judge their peers by the cleanliness of their workspaces. (Source: Adecco) Finding and Interpreting Mean, Variance, and Standard Deviation In Exercises 31–36, find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results and determine any unusual values. 31. Penalty Shots Thirty-three percent of penalty shots in the National Hockey League are converted. The random variable represents the number of penalty shots converted out of six randomly chosen attempts. (Source: Hockey Reference) 32. SAT Test Multiple choice questions on the SAT college admissions exam have four choices. The random variable represents the number of correct answers when you randomly guess the answer for seven questions. 33. Life on Other Planets Seventy-nine percent of U.S. adults believe that life on other planets is plausible. You randomly select eight U.S. adults and ask them whether they believe that life on other planets is plausible. The random variable represents the number who believe that life on other planets is plausible. (Source: Ipsos) 34. Cloning Eighty-five percent of U.S. adults believe cloning humans is morally wrong. You randomly select 10 U.S. adults and ask them whether they believe cloning humans is morally wrong. The random variable represents the number who believe cloning humans is morally wrong. (Source: Gallup) 35. Late for Work Thirty-one percent of U.S. employees who are late for work blame oversleeping. You randomly select 12 U.S. employees who are late for work and ask them whether they blame oversleeping. The random variable represents the number who are late for work and blame oversleeping. (Source: CareerBuilder) 36. Supreme Court Ten percent of college graduates think that Judge Judy serves on the Supreme Court. You randomly select 10 college graduates and ask them whether they think that Judge Judy serves on the Supreme Court. The random variable represents the number who think that Judge Judy serves on the Supreme Court. (Source: CNN)
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