A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 41 months and a standard deviation of 4 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 29 and 37 months? _____% ?

Find the corresponding z-scores for the given number of months of service for the fleet of cars. $$ z=\frac{x-\mu}{\sigma} $$ When x = 29 months, $$ z_1=\frac{29-41}{4}=-3 $$ $$ z_2=\frac{37-41}{4}=-1 $$ Using the 68-95-99.7 rule, P(29 < x < 41) = P(-3 < z < 0) = 99.7% / 2 = 49.85% P(37 < x < 41) = P(-1 < z < 0) = 68% / 2 = 34% Subtract these obtained percentages. P(29 < x < 37) = 49.85% - 34% = 15.85% Therefore, 15.85% of cars remain in service.