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 percentage of 1-mile long roadways with potholes numbering between 28 and 63, we can apply the empirical rule, which states that for a normal distribution: - About 68% of the data falls within one standard deviation of the mean. - About 95% falls within two standard deviations. - About 99.7% falls within three standard deviations. Given the mean is 49 and the standard deviation is 7: 1. **Calculating boundaries**: - One standard deviation below the mean: \(49 - 7 = 42\) - One standard deviation above the mean: \(49 + 7 = 56\) - Two standard deviations below the mean: \(49 - 2(7) = 35\) - Two standard deviations above the mean: \(49 + 2(7) = 63\) - Three standard deviations below the mean: \(49 - 3(7) = 28\) - Three standard deviations above the mean: \(49 + 3(7) = 70\) 2. **Determining intervals of interest**: - The potholes range between 28 and 63, which is within three standard deviations. By the empirical rule, since this range encompasses up to three standard deviations from the mean, approximately **99.7%** of the values will fall between 28 and 63. Therefore, the answer is: ans \( = 99.70 \)