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 11% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 67 returns, what is the probability that she makes errors on:

a. More than 7 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability

b. At least 7 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability

c. Exactly 7 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Probability

Explanation / Answer

This is a binomial distribution problem.
proportion of error, p = 0.11, n = 67
Using a TI calculator,
a) P(X > 7) = 1 - P(X<=7) = 1 - binomcdf(67, .11, 7) = 1 - 0.54064 = 0.46

b) P(X >= 7) = 1 - P(X <= 6) = 1 - binomcdf(67, .11, 6) = 1 - 0.38487 = 0.62

c) P(X = 7) = nCr*pr*(1-p)n-r = 67C7*0.117*0.8960 = 0.1558 = 0.16

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