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 59 months and a standard deviation of 11 months. Using the 68-95-99.7% rule, what is the approximate percentage of cars that remain in service between 26 and 37 months?

Answer 1

2.35%

Explanation:

First, calculate the difference between mean and the months in the problem:

first month :59 – 26 = 33

second motnh: 59 – 37 = 22

Since standard deviation is 11 months, for the first month is a difference of 3 standard deviation and for the second is 2 standard deviation.

the 68-95-99.7% rule establish that:

1 standard deviation means a 68% of total area under the normal distribution. On one side is half = 34%.

2 standard deviations means a 95% of total area under the normal distribution. On one side is half = 47.5%.

3 standard deviation means a 99.7% of total area under the normal distribution. On one side is half = 49.85%.

The difference between 3 and 2 standard deviation is

49.85 – 47.5 = 2.35%

The answer is 2.35% of cars that remain in service between 26 and 37 months