The average length of a hospital stay in general or community hospitals in the United States is 5.5 days. Assuming a population standard deviation of 2.5 days and a simple random sample of 50 patients, what is the probability that the average length of stay for this group of patients will be no more than 6.5 days? If the sample size had been 8 patients instead of 50, what further assumption(s) would have been necessary in order to solve this problem?