SOLUTION: 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 46 and a standard deviation o

Question 1188632: 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 46 and a standard deviation of 11. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 35 and 79?

Found 2 solutions by Solver92311, Shin123:
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

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Answer by Shin123(626) (Show Source): You can put this solution on YOUR website!
The z-scores are and respectively. By the empirical rule, 68% of data falls within 1 standard deviation of the mean, and 99.7% falls within 3. Since the normal distribution is symmetrical around the mean, 34% of data falls between , and 49.85% of the data falls between and .
Therefore, 34%+49.85%=83.85% of 1-mile long roadways have between 35 and 79 potholes.
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