Quantitative Reasoning

Question

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 51 months and a standard deviation of 7 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 30 and 37 months?

_____ % to one decimal place

Answer 1

The 68-95-99.7 rule looks like this:

51 - 1 std dev = 51 - 7 = 44

51 - 2 std dev = 51 - 14 = 37

51 - 3 std dev = 51 - 21 = 30

So we see that the area in question is between -2 std dev and -3 std dev which is 2.35% or, to 1 decimal point, 2.4%