Question

Dottie’s Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 7% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 80 returns, what is the probability that she makes errors on:

1. More than six returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

2. At least six returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

3. Exactly six returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Answer 1

Let X denote the number of errors made in 80 returns Then X follows a Normal distribution with mean- unp- 80x5.6 100 2.2821. 100 100 X-5.6 o 22821 Then Z-X-μ follows Standard Normal ( a) P(X>6)- P (X>6.5) (Continuity correction ) X-5.6 6.5-5.6 2.2821 2.2821 -P(Z>0.39) = 1-P(z 0.39) =1-0.6517 0.3483 (b)P(X26) =P(X>5.5) (Continuity correction) X - 5.65.5-5.6 2.2821 2.2821 P (Z>-0.04 1-P (Z3-0.04) 1-0.484 - 0.516 (c) P(X-6)- P (5.5 <X <6.5) (Continuity correction) P X <6.5)- P(X <5.5) X - 5.6 6.5-5.6 2.2821 2.2821 = P (Z < 0.39)-P(Z <-0.04) Y-5.6 5.5-5.6 2.2821 2.2821 = 0.6517-0.484 -0.1677