The us department of transportation requires tire manufacturers to provide tire performance information on the sidewall of the tire to better inform prospective customers as they make purchasing decision one very important measurement of tire performance is that thread where index which indicates the tires resistance to tread wear compared with a tire grade with a base of 100 a tire with the great of 200should last twice as long on average as a tire graded with a base of 100 a customer organization wants to estimate the actual thread we're index of a brand name of tires that claims graded 200 on the side wall of the tire a random sample of an n= 18 indicates a sample mean tread wear index of 195. 3 and a sample standard deviation 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 dish manufacturer under this branding. b do you think that the customer organization should have to use the manufacturer of producing tires that do not meet the performance information provided on the sidewall of the tires explained. c explain why and observe tierd where index of 210 for a popularity tire is not unusual even through it is outside the confidence interval developed in (a).