Question

1. Gas Mileage Problem
The EPA efficiency rating Ina particular model of new car says that the car is expected to get 22.7 miles per gallon (mpg) of gasoline. Assume that the standard deviation is 1.4 mpg and that the actual mileage are normally distributed about 22.7. The factory produces 2000 of this model.

a. How many of the cars would be expected to get above 23 mpg?
My answer: 830 cars
b. How many would be expected to get below 20 mpg?
My answer: 54 cars
c. How many would be expected to get mileages in the interval from 21 to 24 mpg?
My answer: 1422 cars
d. In what interval about 22.7 could you expect 80% of the mileage to be?
My answer: between 20.9 and 24.5
e. If you purchase one of the cars at random, what is the probability that it will get at least 21.5 mpg?
My answer: 80.4%
f. Suppose you purchased a car of this model and it got only 17.2 mpg. If dealer's service manager told you that this low a mileage was normal for this model car, how would you refute his claim based on statistic? I am stunt on this!

Answer 1

(a)-(d) correct
(e) 17.2 is 3.93 std below the mean
There's almost zero chance of any car getting mileage that low. Most Z tables stop at 3.4 std below the mean, which is 0.03%

Run far, run fast from that dealer!!!