Question 1206704: 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 48 months and a standard deviation of 6 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 54 and 66 months?
Do not enter the percent symbol.
ans =
Answer by ikleyn(52798)   (Show Source):
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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 48 months and a standard deviation of 6 months.
Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 54 and 66 months?
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Notice that in this problem 66 is two standard deviations from the mean of 54.
The Empirical Rule states that 95% of data observed following a normal distribution
lies within 2 standard deviations of the mean.
Since the normal distribution is symmetric, we may conclude that the percentage of cars
that remain in service between 54 and 66 months is half of 95%, i.e. 47.5%. ANSWER
Solved.
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