# 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 = 25.25 mpg and a standard deviation of σ = 2.00 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 _________

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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 = 25.25 mpg and a standard deviation of σ = 2.00 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 _________

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Step 1

Note: X- (X-bar) is considered as X-bar.

a.Finding the standard error of X-bar, the mean from a random sample of 9 fill-ups by one driver:

The standard error of X-bar is σ/sqrt(n).

The standard deviation, σ = 2.00 and n = 9.

Thus, the standard error of X-bar, the mean from a random sample of 9 fill-ups by one driver is, σ/sqrt(n) = 2/sqrt(9) = 0.6667.

Step 2

b. finding the interval within which the sample mean will fall with 95% probability:

A 95% confidence interval for the true mean is as follows:

Step 3

It is given that, X-bar = 25.25 and n = 9.

The degrees of freedom is, n-1 = 9-1 =8.

For a 95% confidence level, the value of tα/2  calculated usi...

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