A company has a policy of retiring company cars.

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 11 months. Using the 68-95-99.7 (Empirical) Rule, what is the approximate percentage of cars that remain in service between 73 and 84 months?

The approximate percentage of cars that remain in service between 73 and 84 months is  %

Answer 1

Hi Bailey,

The 68-95-99.7 rule states that 68% of data falls within one standard deviation of mean, 95% falls within two, and 99.7% falls within three. Draw out the distribution and label the sections. 73 is two standard deviations from your mean of 51. 84 is three standard deviations away. That means that the value you want is between 95 and 99.7% of the distribution BUT:

remember that this is on only one side--the right (positive) side. So:

99.7-95=4.7

We have to divide by 2 to eliminate the left side:

4.7/2=2.35

2.35% of cars remain in service between 73 and 84 months. The picture of the distribution is usually the key with these types of problems.