standard normal distribution

Question

A company has a policy of retiring company cars; this policy looks at the number of miles driven, the purpose of trips, the style of the 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 47 months and a standard deviation of 11 months. Using the 68-95-99.7 (Empirical) Rule, what is the approximate percentage of cars that remain in service between 58 and 80 months?

The approximate percentage of cars that remain in service between 58 and 80 months is  %. Do not enter the percent symbol.)

Answer 1

You want to know the range in terms of standard deviations from the mean (or z = (x - μ)/σ). The rule of 68-95-99.7 refer to the areas for the +/- 1, +/- 2, and +/- 3 sigmas from the mean.

You are given a range from (58-47)/11 = 1 (sigma) to (80-47)/11 = 3 sigma. This is on the right side of the distribution, only, so we divide the the areas by 2 before we compare them. In this case the area is (99.7-68)/2

or 15.85.

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