Anderson Area Hospital administration have recently received an internal audit r
ID: 2925835 • Letter: A
Question
Anderson Area Hospital administration have recently received an internal audit report indicating that 15% of all patient bills contain an error of one form or another. After spending considerable effort to improve the hospital's billing process, the administrators are convinced that things have improved. They believe that the new error rate is somewhere closer to 0.05. A. Suppose that recently the hospital randomly sampled 10 patient bills and conducted a thorough study to determine whether an error exists. It found 3 bills with errors. Assuming that managers are correct that they have improved the error rate to 0.05, what is the probability that they would find 3 or more errors in a sample of 10 bills? B. Referring to part A, what conclusion would you reach based upon the probability of finding 3 or m ore errors in the sample of 10 bills?Explanation / Answer
P = 0.05
n = 10
P( X > 3) = 1 - P ( X < 3)
= 1 - (P (X = 0) + P(X = 1) + P( X =2))
= 1 - (10C0 * (0.05)^0 * (0.95)^10 + 10C1 * (0.05)^1 * (0.95)^9 + 10C2 * (0.05)^2 * (0.95)^8
= 1 - 0.9885 = 0.0115
B) since Probability is less than 0.05, so the event is very unusual.