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 55 months and a standard deviation of 8 months. Using the Empirical Rule rule, what is the approximate percentage of cars that remain in service between 63 and 71 months?

Use same name.

Please only post your questions once. Repeating posts will not get a quicker response. In addition, it wastes our time looking over reposts that have already been answered in another post. Thank you.

See your later post.

To solve this problem using the Empirical Rule, we need to consider the mean and standard deviation of the distribution of the number of months in service for the company cars.

The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

Given that the mean is 55 months and the standard deviation is 8 months, we can calculate the range within two standard deviations of the mean.

Two standard deviations from the mean would be 2 * 8 = 16 months. So, the range within two standard deviations is from 55 - 16 = 39 months to 55 + 16 = 71 months.

Therefore, the approximate percentage of cars that remain in service between 63 and 71 months can be estimated as the difference between the maximum and minimum percentages within two standard deviations.

To calculate this percentage, we calculate the percentage of cars between 39 and 71 months and subtract the percentage of cars between 39 and 63 months.

The percentage of cars between 39 and 71 months is approximately 95% as per the Empirical Rule.

The percentage of cars between 39 and 63 months is approximately 68% as per the Empirical Rule.

Therefore, the approximate percentage of cars that remain in service between 63 and 71 months is approximately 95% - 68% = 27%.

So approximately 27% of the cars would remain in service between 63 and 71 months according to the Empirical Rule.