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 = 20.50 mpg and a standard deviation of = 3.00 mpg. (a) What is the standard error of XX , the mean from a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.)

(b) Within what interval would you expect the sample mean to fall, with 99 percent probability? (Round your answers to 4 decimal places.)