The Central Limit Theorem permit a whole class of distributions, sampling distributions.

    A sampling distribution has the same mean as the source or original distribution, but, it's standard deviation, called the standard error of the mean is different.

    Even if the source distribution is not normal, the sampling distribution will be normal as long as the sample is randomly chosen and the sample size, n, is 30 or greater but less than 10% of the original distribution.

    This normality is VERY useful because the distribution of scores of a normal distribution is known, and readily available to determine confidence interval and perform hypothesis tests.