Question

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 u=25.00 mpg and a standard deviation of o=1.75 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.)

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

Answer 1

Given that, mean (μ) = 25.00 mpg and

standard deviation = 1.75 mpg

a) For sample size (n) = 16, the standard error of is,

=> Standard error of is 0.4375

b) We want to find the, values of and such that,

First we find, the z-score such that, P(-z < Z < z) = 0.90

=> 2 * P(Z < z) - 1 = 0.90

=> 2 * P(Z < z) = 1.90

=> P(Z < z) = 0.95

Using standard normal z-table we get z-score corresponding probability of 0.95 is, z = 1.645

=> P(-1.645 < Z < 1.645) = 0.90

For z = -1.645

For z = 1.645

Therefore, the interval is from 24.2803 to 25.7197 mpg