11-22. Assume that miles per gallon of gasoline for imported passenger cars

(of a given engine displacement) are normally distributed with a known standard deviation of 3.1 miles per gallon, and a comparable figure for domestic vehicles having the same displacement is 4.7 miles per gallon.

Suppose that nX = 42 imported and nY = 50 domestic cars are sampled and their average miles per gallon are 23.5 and 20.1, respectively. Find a 99% confidence interval for the difference μX − μY.