Question

Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants,...

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 12% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 64 returns, what is the probability that she makes errors on:

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

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

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

Homework Answers

Answer #1

We have here given , n = 64 , p = 0.12

np = 64 * 0.12 = 7.68 > 5

n(1-p) = 64 * (1-0.12) = 56.32 > 5  

We can use here normal approximation to binomial

a)  

the probability that she makes errors on: More than 8 returns

P[X>8]

=P[X>8.5]...................by using continuity correction

=P[Z>0.32]

=1-0.6255.....................by using normal probability table.

=0.3745

b) the probability that she makes errors on At least 8 returns

=P[X>7.5]...........................using continuity correction.

=P[Z>-0.07]

=1-0.4721.................................by using normal probability table.

=0.5279

c) P[X=8]

=0.5279-0.3745

=0.1534

Or alternatively ,

P[X=8]

=P[7.5<X<8.5]................................using continuity correction.

=P[-0.07<Z<0.32]

=0.6255-0.4721.......................by using normal probability table.

=0.1534

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