The highway fuel economy of a 2016 Lexus RX FWD 6-cylinder 3.5 automatic 5-speed using premium fuel is a normally distributed random variable with a mean of U = 20.50 mpg and a standard deviation of Q = 1.25 mpg.

(a) What is the standard error of X, the mean from a random sample of 16 fill-ups by one driver? (Round your answer to 4 decimal places).)

Standard error of X _____________

(b) Within what interval would you expect the sample mean to fall, with 90 percent probability? (Round your answer to 4 decimal places.)

The interval is from ____________ to _____________