1. The sales managerof Healthy Plus wants to study customers' spending onhealth products. A survey of the store's customers is designed in order to estimate the proportion of customers who purchase theirhealth supplementsprimarily fromHealthy Plus and the mean yearly amount that customers spend onhealth supplements. A previous survey found that the standard deviation of the amount customers spend onhealth supplements in a month is approximately $15. What sample size is needed to have 95% confidence of estimating the population mean to within $2?

(b) The Transportation Association requires tire manufacturers to provide tire performance information to better inform prospective customers. One veryimportant measure of tire performance is the tread wear index, which indicates the tire's resistance to tread wear. A random sample of 18 tires taken from a local tire manufacturer indicates a mean tread wear index of 195.3 and a standard deviation of 21.4. 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.

(c) The use of mobile devices raises new questions about the intrusion of work into personal life. In a survey by a career company, 158 of 473 employees responded that they typically took work with them on vacation, and 85 responded that there are unwritten and unspoken expectations that they stay connected during vacation. Construct a 95% confidence interval estimate for the population proportion of employees who said that there are unwritten and unspoken expectations that they stay connected during vacation.