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 64 months and a standard deviation of 9 months. Using the empirical rule (as presented in the book), what is the approximate percentage of cars that remain in service between 46 and 55 months? Do not enter the percent symbol. ans \( =\square \% \)

To find the percentage of cars that remain in service between 46 and 55 months, we need to first identify how many standard deviations these values are from the mean. The mean is 64 months, and the standard deviation is 9 months. 1. Calculate how many standard deviations 46 and 55 months are from the mean: - For 46 months: \[ z = \frac{46 - 64}{9} \approx -2 \] - For 55 months: \[ z = \frac{55 - 64}{9} \approx -1 \] Now, according to the empirical rule: - Approximately 68% of the data lies within one standard deviation of the mean (55 to 73 months). - Approximately 95% lies within two standard deviations (46 to 82 months). Since 46 months is two standard deviations below the mean and 55 months is one standard deviation below the mean, we can summarize: - The area between 46 and 73 contains about 95% of the data. - The area between 55 and 73 contains about 68% of the data. To find the percentage of cars in the designated interval (between 46 and 55 months): - We take half of the range covered by two standard deviations (95%) minus half of the range covered by one standard deviation (68%). In this case, we approximate the percentage of cars that remain in service between 46 and 55 months as follows: \[ \text{Percentage} = \frac{95\% - 68\%}{2} \approx 13.5\% \] So, rounding might involve slight variations due to symmetry, but you can take it to be around 13.5%. Therefore, the answer is: ans \( = 13.5 \)