7.15 Given a normal distribution with = 100 and = 10, if you select a sample of n= 25, what is the probability that X is a. less than 95? b. between 95 and 97.5? c. above 102.2? d. There is a 65% chance that X is above what value? 7.30 According to Gallups poll on consumer behavior, 36% of Americans say they will consider only cars manufactured by an American company when purchasing a new car. (Data extracted from The Gallup Poll, www.gallup.com, March 31, 2010.) If you select a random sample of 200 Americans, a. what is the probability that the sample will have between 30% and 40% who say they will consider only cars manufactured by an American company when purchasing a new car? b. the probability is 90% that the sample percentage will be contained within what symmetrical limits of the population percentage? c. the probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage? 8.1 If X = 85, = 8, and n = 64, construct a 95% confidence interval estimate for the population mean, . 8.10 The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours. a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. b. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 400 hours? Explain. c. Must you assume that the population light bulb life is normally distributed? Explain. d. Suppose that the standard deviation changes to 80 hours. What are your answers in (a) and (b)? 8.11 If X = 75, S = 24, and n = 36, and assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean, . 8.17 The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of a tire to better inform prospective customers as they make purchasing decisions. One very important measure of tire performance is the tread wear index, which indicates the tires resistance to tread wear compared with a tire graded with a base of 100. A tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims graded 200 on the sidewall of the tire. A random sample of n = 18 indicates a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. a. Assuming that the population of tread wear indexes is normally distributed, construct a 95% confidence interval estimate for the population mean tread wear index for tires produced by this manufacturer under this brand name. b. Do you think that the consumer organization should accuse the manufacturer of producing tires that do not meet the performance information provided on the sidewall of the tire? Explain. c. Explain why an observed tread wear index of 210 for a particular tire is not unusual, even though it is outside the confidence interval developed in (a). 8.32 In a survey of 2,395 adults, 1,916 reported that e-mails are easy to misinterpret, but only 1,269 reported that telephone conversations are easy to misinterpret. (Data extracted from Open to Misinterpretation, USA Today, July 17, 2007, p. 1D.) a. Construct a 95% confidence interval estimate for the population proportion of adults who report that e-mails are easy to misinterpret. b. Construct a 95% confidence interval estimate for the population proportion of adults who report that telephone conversations are easy to misinterpret. c. Compare the results of (a) and (b). 8.37 If you want to be 95% confident of estimating the population proportion to within a sampling error of 0.02 and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed? 8.40 If a quality control manager wants to estimate, with 95% confidence, the mean life of light bulbs to within 20 hours and also assumes that the population standard deviation is 100 hours, how many light bulbs need to be selected