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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 63 and a standard deviation of 8. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 39 and 71?

a) 68
b) 95
c) 99.7
d) 34

User GaspardP
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2 Answers

3 votes

Final answer:

Approximately 95% of the data is within two standard deviations from the mean for a bell-shaped distribution; hence, the percentage of roadways with potholes between 39 and 71 is about 95%.

Step-by-step explanation:

Using the empirical rule for a bell-shaped distribution, we can determine the percentage of 1-mile long roadways with potholes numbering between 39 and 71. The rule states that approximately 68% of the data falls within one standard deviation (±1 SD), 95% within two standard deviations (±2 SD), and 99.7% within three standard deviations (±3 SD) from the mean. Since one standard deviation from the mean is 63 ± 8, this does not cover our range. However, two standard deviations from the mean, which is the range from 63 - 2(8) = 47 to 63 + 2(8) = 79, does fully cover our range of interest from 39 to 71. Therefore, we are interested in the percentage within two standard deviations from the mean, which is approximately 95%.

User Jjtbsomhorst
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8.1k points
3 votes

Answer:

Step-by-step explanation: C is the answer

User KRoy
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