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 37 months and a standard deviation of 4 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 25 and 29 months? Do not enter the percent symbol. ans =

Answer 1

Solution:

Given a bell shaped distribution( NORMAL DISTRIBUTION) with

= 37

= 4

According to the empirical rule , 68% of the data lie within 1 standard deviations from the mean i.e. within - and +

95% of the data lie within 2 standard deviations from the mean , i.e. within - 2 and + 2

99.7% of the data lie within 3 standard deviations from the mean , i.e. within - 3 and + 3

Here ,

25 = 37 - 12 = - 3

29 = 37 - 8 =   - 2

So ,  approximate percentage of cars that remain in service between 25 and 29 month

= Between - 3 and - 2

= 2.35 %

ans = 2.35