Question

Dottie’s Tax Service specializes in tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit of the returns she prepared indicated that an error was made on 4.2 percent of the returns she prepared last year.   

Use the normal approximation to the binomial distribution to answer all parts of this question. Assuming this rate continues into this year and she prepares 44 returns, what is the probability that she makes errors on

a. More than 5 returns? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.)

Probability           

b. At least 5 returns? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.)

Probability           

c. Exactly 5 returns? (Round z-score computation to 2 decimal places and the final answer to 4 decimal places.)

Probability           

Answer 1

a)

Sample size , n =    44      
Probability of an event of interest, p =   0.042      

          
P(X >   5   ) = P(Xnormal >   5.5
Z=(Xnormal - µ ) / σ =    (5.5-1.848)/1.3306)=       2.745
=P(Z >   2.745   ) =    0.0030

b)

Sample size , n =    44      
Probability of an event of interest, p =   0.042      

          
P(X ≥   5   ) = P(Xnormal ≥   4.5
Z=(Xnormal - µ ) / σ =     (4.5-1.848)/1.3306)=       1.993
=P(Z ≥   1.993   ) =    0.0233

c)

0.0233 - 0.0030

= 0.0203

Please let me know in case of any doubt.

Thanks in advance!

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