When n is large the distribution of the sample means will approach a normal distribution.
The central limit theorem (CLT) is a statistical theory that predicts that given a large enough sample size from a population with a certain level of variation, the mean of all the samples from that population will be close to the population mean.
To put it another way, the central limit theorem predicts with absolute certainty the form of the distribution of means when we take repeated samples from a certain population. In particular, the distribution of means derived from repeated sampling will tend toward normality as sample sizes increase.
In other words, when n is large, the distribution of the sample means will resemble a normal distribution if we continually pick independent, random samples of size n from any population.
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