Retail stores measure productivity by examining annual profits per employee in units of 1 thousand dollars per employee. Suppose it is known that the standard deviation for retail stores is, = 3.7, thousands of dollars.

(a) Suppose a random sample of 35 employees gives a mean of 5.04 thousand dollars per employee. [5] Find a 90% confidence interval for , the average annual profit per employee for retail sales. Round your answer to three decimal places.

(b) Suppose that the annual profits at a large retail store with many employees is 4.1 thousands of [5] dollars. Does this suggest that the store's employees are performing less well than at other stores? Explain

(c) Construct a 95% confidence interval for the same situation. Round your answers to three decimal [5] places.

(d) Explain how increasing the confidence level changes the confidence interval.