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 7 percent 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:

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

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

Exactly 6 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 7 percent 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:

Explanation / Answer

This is a binomial variable.
We need to start calculating the probabilities for make between 0 and 7 errors.
C(80 0)*.7^0*.89^80=0.0004
C(80 1)*.7^1*.89^79 = 0.00336

And so on down to 7 you will find these to be
@2 = 0.01373171
@3 = 0.03677218
@4 = 0.07271801
@5 = 0.113244
@6 = 0.14463

total = 0.3827

You'll notice that @6 is the answer to part c =
The answer to part b is simply the 1 -(sum of the calculated prob)-@6 = 0.14463
and part a is just b-c = 0.23807

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