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

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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) About Me  (Show Source):
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Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The z-scores are %2835-46%29%2F11=-1 and %2875-46%29%2F11=3 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 46-1%2A11=35%7D%7D+and+%7B%7B%7B46-0%2A11=46, and 49.85% of the data falls between 46%2B0%2A11=46 and 46%2B3%2A11=79.
Therefore, 34%+49.85%=83.85% of 1-mile long roadways have between 35 and 79 potholes.