5-2 Binomial Probability Distributions 229 In Exercises 25–28, find the probabilities and answer the questions. 25. Whitus v. Georgia In the classic legal case of Whitus v. Georgia, a jury pool of 90 people was supposed to be randomly selected from a population in which 27% were minorities. Among the 90 people selected, 7 were minorities. Find the probability of getting 7 or fewer minorities if the jury pool was randomly selected. Is the result of 7 minorities significantly low? What does the result suggest about the jury selection process? 26. Social Media and Job Applicants Based on a Society for Human Resource Management survey, 36% of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 25 human resource professionals are randomly selected, would 14 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not? 27. Internet Voting Based on a Consumer Reports survey, 39% of likely voters would be willing to vote by Internet instead of the in-person traditional method of voting. For each of the following, assume that 15 likely voters are randomly selected. a. What is the probability that exactly 12 of those selected would do Internet voting? b. If 12 of the selected voters would do Internet voting, is 12 significantly high? Why or why not? c. Find the probability that at least one of the selected likely voters would do Internet voting. 28. Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability. a. Find the probability that none of the selected adults say that they were too young to get tattoos. b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. c. Find the probability that the number of selected adults saying they were too young is 0 or 1. d. If we randomly select five adults, is 1 a significantly low number who say that they were too young to get tattoos? Significance with Range Rule of Thumb. In Exercises 29 and 30, assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. 29. Gender Selection Assume that the groups consist of 36 couples. a. Find the mean and standard deviation for the numbers of girls in groups of 36 births. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is the result of 26 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method? 30. Gender Selection Assume that the groups consist of 16 couples. a. Find the mean and standard deviation for the numbers of girls in groups of 16 births. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is the result of 11 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method? Significance with Range Rule of Thumb. In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments). 31. Hybrids Assume that offspring peas are randomly selected in groups of 10. a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 10.
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