Question

* 26. 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 dis- tribution with u = 28 days and o = 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 twenty-first day. What percentage of the accounts will receive the discount?

Answer 1

TOPIC:Normal distribution.
26iX Define, x = The age of the accounts, (in days), So, XnN (M = 28, 0 = 8 20-28 X -Me 40-28 @ we need to find, P (20 4 x = 4). P (200528 stools 40-28 (2=X-M. 7 =P 71625 1.50). ~ N(SD. = 0 (01.50) - (-1). [0) = cdf of 2 T: (-k) 7 = I (1.50) - {1-$(1)} = 1-1 (k) ; k. 0.9332- {1-0.8413) [2) values are = [0, 7745 [Am] found from the Normal table.

6 Let , k = The age of to which will send letter. (in the the account, the hospital a reminder Says i oe must have, I since the YP (x ak) = 0.15. preminder letters are sent to the oldest L 15 % of the accounts, (ke29.045. =XP (2x, k-28) coils. =Y 1-(4-28.) = 0.15 * ¢ (-28.) -0.85 = P(1-03) x k-28 = 1.036. From Normal table y k= 36.288 & 36. 29 days. one

③ Here, required proportion. = P(x = 21). =P ( X 24-28). = P(Z < – 0.875). = P(0.875). = 1- P(0.875). = 1- 0.8092. . = 10. 1908 1908 dences pequired percentage = = (0.1908 x100) 7. - 19. go8%. Answer mswer