Statistics Essentials For Dummies (21 page)

If the distribution of
is non-normal or unknown, the sampling distribution of all possible sample means,
is
approximately
normal for a sufficiently large sample size.

The larger the sample size (
n
), the closer the distribution of the sample means will be to a normal distribution.

Most statisticians agree that if
n
is at least 30, it will do a reasonable job in most cases.

Two common misconceptions about the CLT:

The CLT is only needed when the distribution of
X
is either non-normal or is unknown. It is not needed if
X
started out with a normal distribution.

The formulas for the mean and standard error of
are not due to the CLT. These are just mathematical results that are always true.

Finding Probabilities for

After you've established through Case 1 or Case 2 (see previous section) that
has a normal or approximately normal distri-bution, you can find probabilities for
by converting the
-value to a
z
-value and finding probabilities using the
Z
-table (Table A-1