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 57 months and a standard deviation of 11 months. Using the empirical (68-95-99.7) rule, what is the approximate percentage of cars that remain in service between 24 and 46 months? Ans = % (Do not enter the percent symbol. This asks for a percentage so do not convert to decimal. For example, for 99%, you would enter 99, not 0.99)

Answer 1

The mean is given as and standard deviation .

And we need to find the approximate percentage of cars that remains in service between 24 and 46 months.

As we know that the normal distributions follows a 68-95-99.7 rule, i.e., 68% of the data is within , 95% of the data is within and 99.7% of the data is within

The 46 months is one standard deviation below the mean:

The 24 months is three standard deviation below the mean:

Percentage(cars that remains in service between 24 and 46 months )

               =13.5%(below 2 standard deviation)+2.35%(below 3 standard deviation)=15.85%

So, approximately 15.85% of cars that remains in service between 24 and 46 months is 15.85%