Dotties Tax Service specializes in federal tax returns for professional clients,

Question

Dotties 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 10 percent of the returns she prepared last year. Assuming this rate continues into this year and she prepares 62 returns. What is the probability that she makes errors on:

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

Probability

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

Probability

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

Probability

Explanation / Answer

Normal Distribution
Mean ( np ) = 6.2
Standard Deviation ( npq )= 62*0.1*0.9 = 2.3622
Normal Distribution = Z= X- u / sd                   

a)
P(X > 6) = (6-6.2)/2.3622
= -0.2/2.3622 = -0.0847
= P ( Z >-0.085) From Standard Normal Table
= 0.5319
b)
P( Atleast 6) = 1 - P( X > 6) = 1 - 0.5319 = 0.4681

c)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 5.5) = (5.5-6.2)/2.3622
= -0.7/2.3622 = -0.2963
= P ( Z <-0.2963) From Standard Normal Table
= 0.38349
P(X < 6.5) = (6.5-6.2)/2.3622
= 0.3/2.3622 = 0.127
= P ( Z <0.127) From Standard Normal Table
= 0.55053
P(5.5 < X < 6.5) = 0.55053-0.38349 = 0.1696  

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