SECTION 4.2 Binomial Distributions 211 16. Cards You draw five cards, one at a time, from a standard deck. You do not replace a card once it is drawn. The random variable represents the number of cards that are hearts. 17. Lottery A state lottery official randomly chooses 6 balls numbered from 1 through 40 without replacement. You choose six numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. 18. Basketball A’ja Wilson, the 2020 WNBA Most Valuable Player, makes a free throw shot about 78% of the time. The random variable represents the number of free throws that she makes on eight attempts. (Source: Women’s National Basketball Association) Finding Binomial Probabilities In Exercises 19–26, find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. 19. Newspapers Thirty-nine percent of U.S. adults have very little or no confidence in newspapers. You randomly select eight U.S. adults. Find the probability that the number who have very little or no confidence in newspapers is (a) exactly six and (b) exactly three. (Source: Gallup) 20. Civil Rights Fifty-nine percent of U.S. adults think that civil rights for Black Americans have improved during their lifetime. You randomly select seven U.S. adults. Find the probability that the number who think that civil rights for Black Americans have improved during their lifetime is (a) exactly one and (b) exactly five. (Source: Gallup) 21. Actuarial Exam Fifty-two percent of candidates taking actuarial Exam P pass the test. You randomly select 10 Exam P candidates. Find the probability that the number of candidates who pass is (a) exactly four, (b) at least seven, and (c) less than five. (Source: Society of Actuaries) 22. Penalty Kicks Argentine soccer player Lionel Messi converts 78% of his penalty kicks. Suppose Messi takes six penalty kicks next season. Find the probability that the number he converts is (a) exactly six, (b) at most three, and (c) more than three. (Source: Transfermarkt) 23. Second-Hand Fashion Fourteen percent of consumers have tried to purchase clothing second-hand rather than new in the past year. You randomly select 11 consumers. Find the probability that the number who have tried to purchase second-hand rather than new clothing is (a) exactly one, (b) at most five, and (c) more than three. (Source: Fashion Revolution) 24. Responsible Consumption Forty-five percent of consumers say it is important that the clothing they buy is made without child labor. You randomly select 16 consumers. Find the probability that the number of of consumers who say it is important that the clothing they buy is made without child labor is (a) exactly eight, (b) at least ten, and (c) less than twelve. (Source: Fashion Revolution) 25. Workplace Drug Testing Five percent of the U.S. workforce test positive for illicit drugs. You randomly select 14 workers. Find the probability that the number who test positive for illicit drugs is (a) exactly two, (b) more than two, and (c) from two to five. (Source: Quest Diagnostics) 26. Pronunciation Sixty-six percent of people pronounce pecan “puh-CON” instead of “PEA-can.” You randomly select 15 people. Find the probability that the number of people who pronounce pecan “puh-CON” is (a) exactly seven, (b) more than seven, and (c) from seven to eleven. (Source: American Pecans)
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