This distribution has a mean of 58 and a standard deviation of 7. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 44 and 79?

Answer 1

Hi Joey, the Empirical rule, using 58 as the mean and 7 as the standard deviation, gives 68 percent between 51 and 65, 95 percent between 44 and 72, and finally, 99.7 percent between 37 and 79.

The percentage for this problem is between two standard deviations to the left and three standard deviations to the right.

Two standard deviations to the left is 44 and three standard deviations to the right is 79.

The approximate percentage of potholes numbering between 44 and 79 is:

Left ------> | right ------------->

13.5 + 34 + 34 + 13.5 + 2.5, or 97.5

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