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 percent 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:

More than 7 returns?

At least 7 returns?

Exactly 7 returns?

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 percent 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:

More than 7 returns?

At least 7 returns?

Exactly 7 returns?

Explanation / Answer

probabilty of error = 0.11

probability that she makes errors on 0 returns = (0.89)67= 0.0009

probability that she makes errors on 1 returns = 67*(0.89)66(0.11) = 0.0034

probability that she makes errors on 2 returns = 67C2*(0.89)65(0.11)2 = 0.0137

probability that she makes errors on 3 returns = 67C3*(0.89)64(0.11)3 = 0.0368

probability that she makes errors on 4 returns = 67C4*(0.89)63(0.11)4 = 0.0727

probability that she makes errors on 5 returns = 67C5*(0.89)62(0.11)5 = 0.1132

probability that she makes errors on 6 returns = 67C6*(0.89)61(0.11)6 = 0.1446

probability that she makes errors on 7 returns = 67C7*(0.89)60(0.11)7 = 0.1558

probability that she makes errors on atleast 7 returns = 0.0009+0.0034+0.0137+0.0368+0.0727+0.1132+0.1446+0.1558 = 0.5411

probability that she makes errors on more than 7 returns = 1- 0.5411 = 0.4589

probability that she makes errors on 7 returns = 0.1558

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