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-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 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-five 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 ____.

Answer 1

= 20

= 1

n = 25

SE = /

= 1/

= 0.2

By Empirical Rule:

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

Substituting values, we get:

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

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

(iiI0 About 99.7% of possible sample means will be in the range between and

So,

Answers are:

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

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

(iiI0 About 99.7% of possible sample means will be in the range between and