Chapter 5 Probability Distributions 213that case? We can, by means of the Central Limit Theorem. The Central
Limit Theorem states that if you have a sample taken from a probability
distribution with mean m and standard deviation s, the sampling distribu-
tion of x is approximately normal with a mean of m and a standard devia-
tion of s/!n. The remarkable thing about the Central Limit Theorem is that
the sampling distribution of x is approximately normal, no matter what the
probability distribution of the individual values is. As the sample size in-
creases, the approximation to the normal distribution becomes closer and
closer. Now you see why the normal distribution is so important in the
fi eld of statistics.
To see the effect of the Central Limit Theorem, you can use the instruc-
tional workbook named The Central Limit Theorem.
CONCEPT TUTORIALS
The Central Limit Theorem
To use the Central Limit Theorem workbook:1 Open the Central Limit Theorem file from the Explore folder.
Enable the macros in the workbook.
2 Review, in the workbook, the concepts behind the Central Limit
Theorem.
3 Click Explore the Central Limit Theorem from the Table of
Contents.
The Central Limit Theorem worksheet opens. See Figure 5-24.