Question

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 65 miles per​ hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 57 miles per hour and 73 miles per hour.​ (Assume the data set has a​ bell-shaped distribution.)

Answer 1

Answer: 95%

Step-by-step explanation

mu = 65 = mean

sigma = 4 = standard deviation

Compute the z score when x = 57

z = (x - mu)/sigma

z = (57 - 65)/4

z = -8/4

z = -2

Repeat for x = 73 and you should get z = 2

This tells us P(65 < x < 73) is equivalent to P(-2 < z < 2) for the mu and sigma values mentioned.

According to the Empirical Rule, roughly 95% of the normally distributed data values are within 2 standard deviations of the mean. In terms of symbols we write P(-2 < z < 2) = 0.95 approximately.

Furthermore, P(65 < x < 73) = 0.95 approximately when mu = 65 and sigma = 4.

About 95% of the vehicles have speeds between 57 mph and 73 mph.