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 eleven times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 27 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of eleven 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.)

Explanation / Answer

1. Possible sample means would be same as he population mean of 27

2. 60% means one standard deviation away from mean and that would give a confidence interval of 27-1 to 27+1 or (26,28)

2. 95% implies 2 standard deviation away from mean and it gives 27-2 to 27+2 or (25,29)

3. Almost all potential means will fall in 99.5% or 3 standard deviations away from mean so it will be 27-3 to 27+3 or (24,30)

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