The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5-speed u

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 = 20.5 MPG and a standard deviation of = 1.25 MPG.

(a)

What is the standard error of formula74.mml , the mean from a random sample of 16 fill-ups by one driver? (Round your answer to 4 decimal places.)

Standard error of formula74.mml

(b)

Within what interval would you expect the sample mean to fall, with 90 percent probability? (Round your answers to 4 decimal places.)

The interval is from

to

Explanation / Answer

Mean = 20.5

Sd = 1.25

A) standard error = sd / sqrt(n) = 1.25 / sqrt(16) = 0.3125

B) Z for 90% confidence interval = Z0.95 = 1.65

Margin of error, E = Z0.95 * standard error = 1.65 * 0.3125 = 0.5156

Confidence interval = (mean + Margin of error)

= (20.5 + 0.5156)

= (19.9844, 21.0156)

The interval is from 19.9844 to 21.0156

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