8. An accountant is studying the time it takes a company to make payments on accounts payable. The mean time it takes to pay off an invoice is 13.8 days with a standard deviation of 4.3 days, and the times are normally distributed.
(a) What is the probability that an account is paid off in less than 16 days?
(b) Find the 95th percentile for the payoff time- that is, a time for which 95% of the
accounts are paid off in less than that time.
(c) The company has just received 29 invoices. Find the probability that the mean payoff
time for these invoices is more than 16 days.