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 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.)

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