A resort hotel administrator is assigned to conduct performance reviews of the 48 guest services representatives at the resort, and the length of time that the administrator typically spends doing each of these performance reviews is normally distributed with a mean of 64.8 minutes and a standard deviation of 17.5 minutes. The administrator is scheduled to meet with 7 guest service representatives today.

a. What is the probability that the administrator will spend an average of less than one hour with each of the representatives?

b. What is the probability that the administrator will spend a total of more than 7.5 hours with all 7 of the representatives?

c. Within what range of values will the middle 99% of average times spent with each of the 7 representatives fall?

d. What is the maximum total length of time the administrator would expect to spend with all 7 guest service representatives today, with a probability of 0.98?