In an article entitled “Fuel Economy Calculations to Be Altered,” James R. Healey indicated that the government planned to change how it calculates fuel economy for new cars and trucks. This is the first modification since 1985. It is expected to lower average mileage for city driving in conventional cars from 10% to 20%. AAA has forecast that the 2008 Ford F-150 would achieve 15.7 mile per gallon (mpg). The 2005 Ford F-150 was tested by AAA members driving the vehicle themselves and was found to have an average of 14.3 mpg.

a. Assume that the mean obtained by AAA members is the true mean for the population of 2008 Ford F-150 trucks and that the population standard deviation is 5 mpg. Suppose 100 AAA members were to test the 2008 F-150. Determine the probability that the average mpg would be at least 15.7.

b. The current method of calculating the mpg forecasts that the 2008 F-150 will average 16.8 mpg.
Determine the probability that these same 100 AAA members would average more than 16.8 mpg while testing the 2008 F-150.

c. The new method is expected to lower the average mileage by somewhere between 10% and 20%.
Calculate the probability that the average obtained by the 100 AAA members will be somewhere between 10% and 20% smaller than the 14.3 mpg obtained during the 2005 trials even if the new method is not employed.