Question

The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 19.5 MPG and a standard deviation of σ = 1.5 MPG.

(a)	What is the standard error of X⎯⎯⎯X , the mean from a random sample of 9 fill-ups by one driver? (Round your answer to 4 decimal places.)

Standard error of X⎯⎯⎯X

(b)	Within what interval would you expect the sample mean to fall, with 95 percent probability? (Round your answers to 4 decimal places.)

The interval is from

to

Answer 1

Solution :

Given that,

= 19.5

= 1.5

(a)

n = 9

= / n = 1.5 / 9 = 1.5 / 3 = 0.5

(b)

Using Empirical rule,

P(  - 2 < X <    + 2 ) = 95%

P(19.5 - 2 * 0.5 < X < 19.5 + 2 * 0.5) = 95%

P(18.5 < X < 20.5) = 95%

The intervl is from 18.5 to 20.5