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 15% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 52 returns, what is the probability that she makes errors on: a. More than 8 returns? (Round your Z-score computation to 2 decimal places and final answer to 4 decimal places.) Probability b. At least 8 returns? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.) Probability c. Exactly 8 returns? (Round your z-score computation to 2 decimal places and final answer to 4 decimal places.) Probability

Answer 1

Mean = np = 52 * 0.15 = 7.8

Standard deviation = sqrt ( n p( 1 - p) )

= sqrt ( 52 * 0.15 * 0.85)

= 2.5749

Using normal approximation,

P(X < x) = P(Z < x - Mean / SD)

a)

P(X > 8) = P(Z > 8.5 - 7.8 / 2.5749) , Using continuity correction

= P(X > 0.27)

= 0.3936

b)

P(X >= 8) = P(Z > 7.5 - 7.8 / 2.5749) , Using continuity correction

= P( Z > -0.12)

= P( Z < 0.12)

= 0.5478

c)

P(X = 8) = P(7.5 < X < 8.5) , Using continuity correction,

= P(X < 8.5) - P(X < 7.5)

= P(Z < (8.5 - 7.8) / 2.5749) - P(Z < (7.5 - 7.8) / 2.5749)

= P(Z < 0.27) - P(Z < -0.12)

= 0.6064 - 0.4522

= 0.1542