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?
note that 63 is 1 std above the mean, and 71 is 2 std above the mean.
To solve this problem using the Empirical Rule, we need to know that for a bell-shaped or normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean is 55 months and the standard deviation is 8 months.
To find the approximate percentage of cars that remain in service between 63 and 71 months, we need to see how many standard deviations away these values are from the mean.
For 63 months:
(63 - 55) / 8 = 1
For 71 months:
(71 - 55) / 8 = 2
Since 63 months is one standard deviation above the mean and 71 months is two standard deviations above the mean, we can use the Empirical Rule to estimate the percentage.
Approximately 68% + 95% = 163% (68% for one standard deviation and 95% for two standard deviations).
However, since we only have a maximum of 100% of cars in service, we can say that approximately 100% - 4% = 96% of cars remain in service between 63 and 71 months.