A car company claims that its only hybrid car has a highway gas mileage of 40 mpg on average. An independent company randomly selects one of the cars, which turns out to have a gas mileage of 38 mpg.
a. Assuming the gas mileages of the cars are approximately normally distributed with mean 40 mpg and standard deviation 0.6 mpg, find the probability that a randomly selected hybrid car manufactured by the company has a gas mileage of at most 38 mpg.
b. If the assumptions you made in part (a) are true, is the randomly selected car’s gas mileage of 38 mpg an unusual event?
c. Describe a scenario in which the randomly selected car’s gas mileage of 38 mpg is not an unusual event.
d. On the basis of the randomly selected car having a gas mileage of 38 mpg, do the assumptions you made in part (a) seem reasonable? Should a more thorough investigation occur?