The IRS computes the time it takes filers to complete its f

. 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 55.5 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 21 of these forms to complete one day. What is the probability that the mean completion time for the 21 forms is over 60 minutes?

Solution

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 55.5 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?

Z value for 60, z = (60-55.5)/11.2 =0.40

P( x >60) = P( z >0.40) =0.3446

(B) Find a time such that 85% of all forms can be completed in less than that time.

Z value for Bottom 85% = 1.036

X= mean+z*sd =55.5+1.036*11.2 = 67.1032

(C) An accounting firm has 21 of these forms to complete one day. What is the probability that the mean completion time for the 21 forms is over 60 minutes?

Standard error = sd/sqrt(n) =11.2/sqrt(21) = 2.444

Z value for 60, z = (60-55.5)/2.444 =1.84

P( mean x >60) = P( z >1.84) = 0.0329