The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 49 and a standard deviation of 7 . Using the empirical rule (as presented in the book), what is the approximate percentage of 1 -mile long roadways with potholes numbering between 28 and 63 ? (Round percent number to 2 decimal places.) Do not enter the percent symbol. ans =

To find the approximate percentage of 1-mile long roadways with potholes numbering between 28 and 63 using the empirical rule, we first find how many standard deviations away these numbers are from the mean. The mean is 49 and the standard deviation is 7. Calculating the z-scores: - For 28: \( z = \frac{28 - 49}{7} = \frac{-21}{7} = -3 \) - For 63: \( z = \frac{63 - 49}{7} = \frac{14}{7} = 2 \) According to the empirical rule: - Approximately 68% of the data falls within 1 standard deviation of the mean (42 to 56). - About 95% falls within 2 standard deviations (35 to 63). - Roughly 99.7% falls within 3 standard deviations (28 to 70). Since 28 to 63 covers 3 standard deviations below the mean to 2 above, the approximate percentage of roadways with potholes numbering between 28 and 63 is around 99.7%. Thus, the answer is: ans = 99.70