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 de

Question 1128019: 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 15% of all forms are 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?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x-mean)/sd
z>(60-55.5)/11.2=4.5/11.2=0.40
probability z>0.40 is 0.3446
z(0.15)=-1.036
x-mean=-1.036*11.2=-11.60
x=55.5-11.60=43.4
for 20 forms, the std error is std dev/sqrt(20)
z>(60-55.5)/11.2/sqrt(20)
z>(4.5)*sqrt*(20)/11.2, or 1.8
That probability is 0.0359

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