We want to survey office product purchasing managers of service companies to obtain an average estimate of the annual amount of office supplies purchased. An initial survey of service firms establishes the order of magnitude of the standard deviation of the annual purchase amount at $800. (a) Determine the number of service companies required to estimate, with 90% confidence, the average annual purchase of office supplies with a margin of error not exceeding $200. It is assumed that the annual purchase amount is normally distributed. b) For the same level of confidence, how many service companies should be contacted to service companies to be contacted to ensure that the margin of error in estimating the average annual purchase of office supplies does not exceed $100?