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 55 and a standard deviation of 9 . Using the empirical rule, what is the approximate percentage of 1 -mile long roadways with potholes numbering between 46 and 82 ? Do not enter the percent symbol. ans =

To find the approximate percentage of 1-mile stretches with potholes between 46 and 82 using the empirical rule, we first need to determine how many standard deviations away from the mean these values are. The mean is 55 and the standard deviation is 9. For 46: \( (46 - 55) / 9 = -1 \) (1 standard deviation below the mean) For 82: \( (82 - 55) / 9 = 3 \) (3 standard deviations above the mean) According to the empirical rule, about 68% of the data falls within 1 standard deviation (between 46 and 64), and about 99.7% falls within 3 standard deviations (between 28 and 82). So, the approximate percentage of 1-mile stretches with potholes between 46 and 82 is about 99.7%. ans = 99.7