A national manufacturer of unattached garages discovered tha

A national manufacturer of unattached garages discovered that the distribution of the lengths of time it takes two construction workers to erect the Red Barn model is normally distributed with a mean of 31 hours and a standard deviation of 3 hours. What percent of the garages take between 31 and 38 hours to erect?

Solution

P(31 <X< 38) = P((31-31)/3<(X-mean)/s <(38-31)/3)

=P(0<Z<2.33)

=0.4902 (from standard normal table)

i.e. 49.02%