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 42 and a standard deviation of 10. Using the empirical (68-95-99.7) rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 22 and 52

81.5% of 1-mile long roadways with potholes numbering between 22 and 52

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 42, standard deviation of 10.

The normal distribution is symmetric, so 50% of the measures are below the mean and 50% are above the mean

Approximate percentage of 1-mile long roadways with potholes numbering between 22 and 52:

22 = 42 - 2*10

So 22 is two standard deviations below the mean. Of the 50% of the measures that are below the mean, 95% are between two standard deviations below the mean(22) and the mean(42).

52 = 42 + 10

So 42 is one standard deviation above the mean. Of the 50% of the measures that are above the mean, 60% are between the mean(42) and one standard deviation above the mean(52).

In the desired interval, the percentage is:

81.5% of 1-mile long roadways with potholes numbering between 22 and 52

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: