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 35 months and a standard deviation of 11 months. Using the empirical rule, what is the approximate percentage of cars that remain in service between 13 and 24 months? Do not enter the percent symbol. ans =

To find the approximate percentage of cars that remain in service between 13 and 24 months using the empirical rule, we first determine how many standard deviations away from the mean these values are. The mean is 35 months, and the standard deviation is 11 months. The limits of 13 and 24 months correspond to: - 13 months: \( (13 - 35) / 11 \approx -2.00 \) standard deviations from the mean. - 24 months: \( (24 - 35) / 11 \approx -1.00 \) standard deviations from the mean. According to the empirical rule (68-95-99.7 rule), approximately 68% of the data falls within 1 standard deviation of the mean and about 95% fall within 2 standard deviations. The range from 13 to 24 months covers from -2 to -1 standard deviations. Therefore, we find the percentage from -2 to the mean, which is half of the 95% for -2 standard deviations. That’s around 47.5%. To get the percentage of cars between 13 and 24 months, we take about half of the 68% (34%), as 13 months is further than 1 standard deviation from the mean. So, the approximate percentage of cars that remain in service between 13 and 24 months is: ans = 34