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The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has...

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 59 and a standard deviation of 11. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 37 and 92? Do not enter the percent symbol. ans = %

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Answer #1

Z score = (x - ) /

Z score for 37 = (37 - 59)/11 = -2

Z score for 92 = (92 - 59)/11 = 3

By empirical rule, the approximate percentage of data lie within 2 standard deviations = 95%

By empirical rule, the approximate percentage of data lie from mean to left of 2 standard deviations = 95/2 = 47.5%

By empirical rule, the approximate percentage of data lie within 3 standard deviations = 99.7%

By empirical rule, the approximate percentage of data lie from mean to right of 3 standard deviations = 99.7/2 = 49.85%

The approximate percentage of 1-mile long roadways with potholes numbering between 37 and 92 is

47.5 + 49.85 =  97.35 %

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