The UCSB Business & Financial Services Office reports that the account balance (money owed) for an undergraduate student at the start of the quarter is normally distributed with a mean of $4,785, and a standard deviation of $345. An internal audit by the UC Board of Regents inspected a random sample of 25 undergraduate student accounts.

a. (4 points) If the UC Board of Regents defines any tuition totals above $4,886.43 as excessive tuition, what is the probability that the sample mean would be classified as excessive tuition?

b. (4 points) The office of financial aid will reduce the amount of financial aid awarded if the tuition bill is lower than the cost of the minimum full-time course load, $4,681.5. What is the probability the sample mean would qualify to have the amount of financial aid reduced?

c. (6 points) What is the probability that the sample mean tuition is either above $4,920.24 or below $4,649.76?