The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5-sp

Question

The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5-speed using regular gas is a normally distributed random variable with a range 28 MPG to 37 MPG.

Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution). (Round your answer to 4 decimal places.)

What sample size is needed to estimate the mean with 90 percent confidence and an error of ± 0.25 MPG? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.)

The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5-speed using regular gas is a normally distributed random variable with a range 28 MPG to 37 MPG.

Explanation / Answer

The empirical rule states:
68% of observations lie within one standard deviation of the mean
95% of observations lie within two standard deviation of the mean
99% of observations lie within three standard deviation of the mean

mean + 2 sd = 37
mean - 2 sd = 28
solving for sd

we get 4sd = 9

or sd = 2.25

b)
z value = 1.645 (for 90% confidence)
Sample size = ( z s / e)^2
sample size = ( (1.645) s / 0.25)^2
substitute the value of s found in (a)
we get sample size = (1.645*2.25/.25)^2 = 219

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