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 10% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 53 returns, what is the probability that she makes errors on. a. More than 5 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) b. At least 5 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) c. Exactly 5 returns? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

Explanation / Answer

X - number of return which makes an error

n = 53 , p =0.1

X is binomial

we will appreoximate it using normal distribution

mean = np = 53*0.1 = 5.3

sd =sqrt(npq) =sqrt(53*0.1*0.9) = 2.18403296

Z = (X - 5.3 )/2.18403296

P(X > 5)

=P(X> 5.5) due to continuity correction

=P(Z> (5.5-5)/2.18403296)

= P(Z> 0.22893 )=0.4095

b) P(X > = 5)

=P(X> 4.5) due to continuity correction

=P(Z> (4.5-5)/2.18403296)

=P(Z > -0.22893) =0.5905

c)P(X =5)

P(4.5 < X< 5.5)   

  due to continuity correction

=P( (4.5-5)/2.18403296 <Z< (5.5-5)/2.18403296 )

=P(-0.22893 < Z< 0.22893 )

=0.1811

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