Central Limit Theorem Machine

The Central Limit Theorem: Let x̄ be the mean of a large (n > 30) simple random sample from a population with mean μ and standard deviation σ. Then the sampling distribution of x̄ is approximately normal, with mean μ_x̄ = μ and standard deviation σ_x̄ = σ/√n. The size of the sample needed to obtain approximate normality depends mostly on the skewness of the population. A sample of size n > 30 is large enough for most populations encountered in practice, and smaller sample sizes are adequate for distributions that are nearly symmetric. A single sample still looks like the population; it is the distribution of the sample means that is approximately normal.