Dottie\'s Tax Service specializes in federal tax returns for professional client

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 15% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 52 returns, what is the probability that she makes errors on:

More than 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

At least 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Exactly 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

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 15% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 52 returns, what is the probability that she makes errors on:

More than 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

At least 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Exactly 8 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Explanation / Answer

p = 0.17
q = 1-p = 1 - 0.17 = 0.83
n = 52

mean = np = 8.84
std. dev. = sqrt(npq) = 2.7087

P(X>=8) = P(z>=(8-8.84)/2.7087) = P(z>-0.3101) = 0.6218

P(X=8) = P(X>=7) - P(X>=8) = P(z>=(7-8.84)/2.7087) - 0.6218
P(X=8) = P(z>=-0.6793) - 0.6218
P(X=8) = 0.7515 - 0.6218 = 0.1297

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