How do banks rate? One way to answer this question is to examine annual profits per employee. Forbes top companies, edited by J.T. Davis (John Wiley & Sons), gave the following data about annual profits per employee (in units of one thousand dollars per employee) for representative companies in financial services. Companies such as Wells Fargo, First Bank System, and Key Banks were included. Assume 10.2 thousand dollars.

42.9 43.8 48.2 60.6 54.9 55.1 52.9 54.9 42.5 33.0 33.6 36.9 27.0 47.1 33.8 28.1 28.5 29.1 36.5 36.1 26.9 27.8 28.8 29.3 31.5 31.7 31.1 38.0 32.0 31.7 32.9 23.1 54.9 43.8 36.9 31.9 25.5 23.2 29.8 22.3 26.5 26.7

(a)Calculate the .(1 mark)

(b) Let us say that the preceding data are representative of the entire sector of (successful) financial services corporations. Find a 75% confidence interval for , the average annual profit per employee for all successful banks.(4 marks)