In: Statistics and Probability
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 μ = 22.00 mpg
and a standard deviation of σ = 1.25 mpg.
(a) What is the standard error of X, the mean from
a random sample of 25 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 98 percent probability? (Round
your answers to 4 decimal places.)
The interval is from __________ to ___________
Solution :
Given that,
mean = = 22.00 mpg
standard deviation = = 1.25 mpg
n = 25
a) = = 22.00
= / n = 1.25 / 25 = 0.25
b) Using standard normal table,
P( -z < Z < z) = 98%
= P(Z < z) - P(Z <-z ) = 0.98
= 2P(Z < z) - 1 = 0.98
= 2P(Z < z) = 1 + 0.98
= P(Z < z) = 1.98 / 2
= P(Z < z) = 0.99
= P(Z < 2.33) = 0.99
= z ± 2.33
Using z-score formula,
= z * +
= -2.33 * 0.25 + 22.00
= 21.4175
Using z-score formula,
= z * +
= 2.33 * 0.25 + 22.00
= 22.5825
The interval is from 21.4175 to 22.5825