Intro to Stats and Analytics

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 59 months and a standard deviation of 9 months. Using the empirical rule, what is the approximate percentage of cars that remain in service between 68 and 77 months?

Use 68-95-99.7 and do not enter the percent symbol.

ans =  %

Answer 1

Hi Lucy,

It really helps for these problems to draw the distribution and label mu, mu + sigma, mu + 2sigma, and mu + 3sigma. I cannot do it here due to character limits but:

mu=59

sigma=9

mu + sigma = 59 + 9 =68

mu + 2sigma 59 + 2(9) =77

So we want the piece between one and two standard deviations from 68. We know that 95% of the data fall within two standard deviations of the mean either way. We also know 68% fall within one either way. We are interested in the space between 68% and 95%, but only for the top half of the data. So:

95 - 68 =27

We must halve this to get only our desired segment above the mean:

27/2 = 13.5% Don't use the symbol.

I hope this helps.