7·The IRS computes the time it takes filers to complete its forms. For a particu

Question

7·The IRS computes the time it takes filers to complete its forms. For a particular form, the completion times are normally distributed with a mean of SS.5 minutes and a standard deviation of 11.2 minutes. (A) What is the probability that it takes an individual filer more than 60 minutes to complete the form? (B) Find a time such that 85% of all forms can be completed in less than that time. (C) An accounting firm has 20 of these forms to complete one day. What is the probability that the mean completion time for the 20 forms is over 60 minutes?

Explanation / Answer

7. We have been given params of normal distribution:

Mean = 55.5 min

Stdev = 11.2 min

A. P(X>60) = P(Z> (60-55.5)/11.2) = P(Z>.402) = .6561

B. P(X<c) = .85

P(Z< c-55.5 / 11.2) = .85

The Z value from Z tables is -1.036

Therefore, (c-55.5)/11.2 = -1.036

c = -1.036*11.2+55.5

=43.897

C. n =20

P(X>60)

= P(t> (60-55.5)/(11.2/sqrt(20))

= P(t> 1.8)

= 0.044

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