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 63 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 30 and 52 months?
Do not enter the percent symbol.
ans =
%

Answer 1

Answer:  15.85%

This value is approximate.

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Explanation:

• mu = 63 = population mean
• sigma = 11 = population standard deviation

Let's convert x = 30 to its corresponding z score

z = (x-mu)/sigma

z = (30-63)/11

z = -33/11

z = -3

This score is 3 standard deviations below the mean.

Repeat for x = 52

z = (x-mu)/sigma

z = (52-63)/11

z = -11/11

z = -1

This score is 1 standard deviation below the mean.

The task of finding P(30 < x < 52) is the same as P(-3 < z < -1)

We converted to z scores so we could use the Empirical Rule.

Refer to the chart below. We'll be focusing on the left green portion that is between z = -3 and z = -2 and the left blue portion which is between z = -2 and z = -1.

Those two approximate areas add to:  (2.35%) + (13.5%) = 15.85%