The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of = 20.25mpg and a standard deviation of = 2.25mpg.

(a)What is the standard error of X

X

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

Standard error ofX

X

________?_____

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

The interval is from? to?