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 10 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 57 returns. What is the probability that she makes errors on:

(a) More than 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

(b) At least 6 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

(c) Exactly 6 returns?

Explanation / Answer

mean=n*p=57*0.1 = 5.7

standard deviation =sqrt(n*p*(1-p)) =sqrt(57*0.1*0.9) =2.26495

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(a) P(X>6) = P((X-mean)/s >(6-5.7)/2.26495)

=P(Z>0.13) =0.4483 (from standard normal table)

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(b) P(X>=6) = P(X>6.5) (by using continuous correction)

=P(Z>(6.5-5.7)/2.26495)

=P(Z>0.35) = 0.3632 (from standard normal table)

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(c) P(X=6)=P(5.5<X<6.5)

=P((5.5-5.7)/2.26495<Z<(6.5-5.7)/2.26495)

=P(-0.09<Z<0.35) =0.1727 (from standard normal table)

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