The average miles per gallon of a particular automobile model are approximately normally distributed with a given mean u = 43.8 miles per gallon and standard deviation o = 5.1 miles per gallon. What percentage of the automobiles have an average miles per gallon between 38.7 miles per gallon and 48.9 miles per gallon?

68

75

95

100

A) 68%

Note that 38.7 mpg is one standard deviation below the mean, and that 48.8 mpg is one std dev above the mean. Thus, we're interested in finding the area under the standard normal curve within one std dev of the mean.

According to the Empirical Rule, that percentage is 68%.

Thus, 68% of cars in this pool get between 38.7 and 48.8 mpg.