# A confidence interval of the mean

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Let's summarize the method for finding the 95% confidence interval using a step-by-step illustration. Suppose that a certain automobile company wishes to determine the expected miles per gallon for one of its new models. Based on years of experience with cars, the company statistician realizes that not all cars are equal, and that a standard deviation of 4 miles per gallon ( = 4) is to be expected due to variations in parts and workmanship. In order to estimate the mean miles per gallon for the new model, he test runs a random sample of 100 cars off the assembly line and obtains a sample mean of 26 miles per gallon.

What steps are followed to obtaining a 95% confidence interval for the mean miles per gallon for all cars of this model?

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#### Solution Preview

STEP 1

Obtain the mean for a random sample (in this problem, it is given).

N=100, X=26

STEP 2

Calculate the standard error of the mean (knowing that standard deviation = 4).

standard error of the mean

= ...

#### Solution Summary

Steps are given to solve this problem.