The Central Limit Theorem tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases. In practice, the distribution of the sample means approaches a bell-shape curve when n > 30. More specifically speaking, if a random variable X has a mean of µ and a standard deviation of σ, then the sample means are approximately normally distributed with a mean of µ and a standard deviation of [tex] \frac{\sigma}{ \sqrt{n} } [/tex] as the sample size increases.
