Applying the Central Limit Theorem in R, The central limit theorem states that if the sample size is high enough, the sampling distribution of a sample mean is approximately normal, even if the population distribution is not. The sample distribution will also have the following properties, according to the central limit theorem: The sample distribution’s mean will be equal to the population distribution’s mean. x = μ The sampling distribution’s standard deviation will be equal to the population distribution’s standard deviation divided by the sample size.