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umka2103 [35]
2 years ago
14

The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This dist

ribution has a mean of 47 and a standard deviation of 7. Using the empirical rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 40 and 68?
Mathematics
1 answer:
alexira [117]2 years ago
5 0
<h3>Answer:   83.85%</h3>

This value is approximate.

==========================================================

Explanation:

Let's compute the z score for x = 40

z = (x-mu)/sigma

z = (40-47)/7

z = -1

We're exactly one standard deviation below the mean.

Repeat these steps for x = 68

z = (x-mu)/sigma

z = (68-47)/7

z = 3

This score is exactly three standard deviations above the mean.

Now refer to the Empirical Rule chart below. We'll add up the percentages that are between z = -1 and z = 3. This consists of the two pink regions (each 34%), the right blue region (13.5%) and the right green region (2.35%). These percentages are approximate.

34+34+13.5+2.35 = 83.85

<u>Roughly 83.85%</u> of the one-mile roadways have between 40 and 68 potholes.

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