General Hospital’s patient account division has compiled data on the age of accounts receivable. The data collected indicate that the age of the accounts follows a normal distribution with µ= 28 days and σ = 8 days.

a. What portion of the accounts is between 20 and 40 days old—that is, P(20 ≤ x ≤ 40)?

b. The hospital administrator is interested in sending reminder letters to the oldest 15% of accounts. How many days old should an account be before a reminder letter is sent?

c. The hospital administrator wants to give a discount to those accounts that pay their balance by the 21st day. What percentage of the accounts will receive the discount?