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 47 months and a standard deviation of 5 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 57 and 62 months?

Answer 1

Given that, mean = 47 months and

standard deviation = 5 months

We want to, find the percentage of cars that remain in service between 57 and 62 months.

for x = 57

z = (57 - 47)/5 = 10/5 = 2

for x = 62

z = (62 - 47)/5 = 15/5 = 3

By rule ii) 95/2 = 47.5% of the data fall between mean and 2 standard deviations above the mean. That is 47.5% of the data fall between 47 and 57.

By rule iii) 99.7/2 = 49.85% of the data fall between mean and 3 standard deviations above the mean. That is 49.85% of the data fall between 47 and 62.

Therefore, the percentage between 57 and 62 is, 49.85 - 47.5 = 2.35%

Hence, the percentage of cars that remain in service between 57 and 62 months is 2.35%

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Note : According to 68-95-99.7 rule,

i) Approximately 68% of the data fall within 1 standard deviations of the mean.

ii) Approximately 95% of the data fall within 2 standard deviations of the mean.

iii) Approximately 99.7% of the data fall within 3 standard deviations of the mean.