Question

A company has a policy of retiring company cars; this policy looks at the number of miles driven, the 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 42 months and a standard deviation of 10 months. Using the 68-95-99.7 rule, what is the approximate percentage ofcars that remain in service between 52 and 72 months.

Answer 1

Step-by-step explanation

We have the following facts:

Mean = 42

Standard Deviation = 10

We can see that 52 is 1 standard deviation to the right of the mean.

Furthermore, 72 is 3 standard deviations to the right of the mean.

Also, the Empirical Rule has 68% between 1 standard deviation and 34% on one side. Additionally, it has 95% between two standard deviations or 47.5% on one side.

Moreover, It has 99.7% within 3 sd or 49.85% on one side.

Following this reasoning, we can affirm that between 3 standard deviations and 1 standard deviation there are 49.85-34=15.85%