Question

8.8 The Highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is normally distributed random variable with mean of µ = 27.0 mpg and a standard deviation of ? = 1.25 mpg: (a) What is the standard area of X ?, the mean from a random sample 16 fill-ups by one driver? (b) Within what interval would you expect the sample mean to fall with 90 percent probability?

Answer 1

(a)

= 27

= 1.25

n = 16

SE = /

= 1.25/ = 0.3125

So,

standard deviation of the distribution of , the sample mean = SE = 0.3125

(b) 90% probability corresponds to area = 0.90/2 = 0.45 from mid value to either side.Table of Area Under Standard Normal Curve gives Z = 1.645

Low side:
Z = - 1.645 = ( - )/SE

- 1.645 = ( - 27)/0.3125

So,

X = 27 - (1.645 X 0.3125)

   = 27 - 0.5141

= 26.4859

High side:

X = 27 + 0.5141

   = 27.5141

So,

the required interval is:

(26.4859, 27.5141)