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 μ = 25.75 mpg and a standard deviation of σ = 2.75 mpg.

(a) What is the standard error of X bar , the mean from a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.)
  
Standard error of X bar   

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

Answer 1

Here we have : μ = 25.75, σ = 2.75

a) n = 36

The standard error is given by,

SE =

= 0.4583

b) The point estimate of mean = μ = 25.75

The 99% confidence interval is given by,

( - E , + E )

So,

c = 0.99,

------------- ( We use excel formula "=norm.s.inv(0.995)" )

= 1.1824

Hence the 99% confidence interval is given by,

( 25.75 - 1.1824 , 25.75 + 1.1824 )

( 24.5676 , 26.9324 )

The interval is from 24.5676 to 26.9324.