Suppose that you are interested in estimating the average number of miles per ga

Question

Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-three times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 21 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-three observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)

About 68% of possible sample means will be in the range between ( )and ( ) .

About 95% of possible sample means will be in the range between  ( )and ( )

About 99.7% of possible sample means will be in the range between ( )and ( )  

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

here as std error =std deviation/(n)1/2 =1/(23)1/2 =0.209

1) as 68% values fall with in one std error

About 68% of possible sample means will be in the range between 20.791 and 21.209

2)

95% values fall with in two std error

About 95% of possible sample means will be in the range between 20.582 and 21.418

3)

99.7% values fall with in three std error

About 99.7% of possible sample means will be in the range between 20.373 and 21.627

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