With the high cost of fuel and intense competition, the major airline companies have had a very difficult time financially in recent years. Many carriers are now charging for checked bags. One carrier is considering charging a two-tiered rate based on the weight of checked bags. Before deciding at what rate to increase the charge, the airline wishes to estimate the mean weight per bag checked by passengers. It wants the estimate to be within ± 0.25 pounds of the true population mean. A pilot sample of bags checked gives the following results:

a. What size sample should the airline use if it wants to have 95% confidence?
b. Suppose the airline managers do not want to take as large a sample as the one you determined in part a. What general options do they have to lower the required sample size?