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 54 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 40 and 61?
Do not enter the percent symbol.
ans =?

The empirical rule states for a normal distribution:

68% of the data are within ± 1 standard deviation from the mean

95% of the data are within ± 2 standard deviations from the mean

99.7% of the data are within ± 3 standard deviations from the mean

A normal distribution is also symmetric around its mean. Since that's the case, 34% (1/2 of 68) would be within +1 standard deviation from the mean and 34% would be within -1 standard deviation from the mean

This problem asks what is the percentage between 53 and 65 when the mean is 62 and the standard deviation is 3. Putting this in terms of the mean and standard deviations, this problem asks what is the percentage between -3 and + 1 standard deviations?

The percentage between the mean and -3 standard deviations is 49.85% (this is one half of 99.7%)

The percentage between the mean and +1 standard deviations is 34% (one half of 68%)

Add those two together to get your total percentage

no this is a nonlinear negative