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 35 and a standard deviation of 9 . Using the empirical rule (as presented in the book), what is the approximate percentage of 1 - mile long roadways with potholes numbering between 26 and 62 ? Do not enter the percent symbol. ans =

We are given that the number of potholes on a 1‑mile stretch of freeway pavement is bell-shaped (approximately normal) with a mean (μ) of 35 and a standard deviation (σ) of 9. The question asks for the approximate percentage of roadways having a pothole count between 26 and 62. Step 1: Convert the endpoints of the range to z-scores. • For the lower limit (26):   z = (26 – 35) / 9 = –9 / 9 = –1. • For the upper limit (62):   z = (62 – 35) / 9 = 27 / 9 = 3. Step 2: Apply the empirical rule. - The empirical rule states that about 68% of data lie within 1 standard deviation of the mean (i.e., between z = –1 and z = +1), about 95% lie within 2 standard deviations, and about 99.7% lie within 3 standard deviations. - The percentage below z = –1 is approximately 16% (since 50% – 34% ≈ 16%). - The percentage below z = 3 is approximately 99.85% (or nearly 100%). Thus, the percentage of observations between z = –1 and z = 3 is approximately:   99.85% – 16% ≈ 84%. Therefore, the approximate percentage of 1‑mile roadways with pothole counts between 26 and 62 is 84. Final Answer: 84