The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has an approximate normal distribution with mean 39 and a standard deviation 3. Use the Empirical Rule to determine the approximate proportion of 1-mile long roadways with potholes numbering between 36 and 45?

Question

Mathematics

Emilee Woods

3 November, 13:35

The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has an approximate normal distribution with mean 39 and a standard deviation 3. Use the Empirical Rule to determine the approximate proportion of 1-mile long roadways with potholes numbering between 36 and 45?

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Watson · Answer 1

Step-by-step explanation:

The Empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean. The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 39 and the standard deviation is 3.

99.7% of the number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania would fall within one standard deviation.

standard deviations = 3

39 - 3 = 36

39 + 3 = 42

Therefore, the approximate proportion of 1-mile long roadways with potholes numbering between 36 and 45 is 0.997