The New York Times reported that 17.2 million new cars and light trucks were sold in the United States in 2017, and the U.S. Environmental Protection Agency projects the average efficiency for these vehicles to be 25.2 miles per gallon. Assume that the population standard deviation in miles per gallon for these automobiles is σ = 6. 

a. What is the probability a sample of 70,000 new cars and light trucks sold in the United States in 2017 will provide a sample mean miles per gallon that is within .05 miles per gallon of the population mean of 25.2? 

b. What is the probability a sample of 70,000 new cars and light trucks sold in the United States in 2017 will provide a sample mean miles per gallon that is within .01 miles per gallon of the population mean of 25.2? Compare this probability to the value computed in part (a). 

c. What is the probability a sample of 90,000 new cars and light trucks sold in the United States in 2017 will provide a sample mean miles per gallon that is within .01 of the population mean of 25.2? Comment on the differences between this probability and the value computed in part (b). 

d. Suppose the mean miles per gallon for a sample of 70,000 new cars and light trucks sold in the United States in 2017 differs from the population mean μ by more than one gallon. How would you interpret this result?