Based on annual driving of 15000 miles and fuel efficiency o

Based on annual driving of 15,000 miles and fuel efficiency of 20 mpg, a car in the United States uses, on average, 720 gallons of gasoline per year. If annual automobile fuel usage is normally distributed, and if 21.77% of cars in the United States use less than 520 gallons of gasoline per year, what is the standard deviation?

(Round your answer to 2 decimal places.)

Solution

For a left tailed area of 0.2177, the corresponding z score is

z = -0.779984498

Thus, as

sigma = (x-u)/z

Then

sigma = (520-720)/-0.779984498 = 256.4153525 = 256.42 [ANSWER]