gen-in-3-4-sentences-explain-the-central-limit-theorem-state-any-a33c

In 3-4 sentences, explain the central limit theorem. State any key formula.

The Central Limit Theorem states that when you take sufficiently large random samples from any population with mean μ and standard deviation σ, the distribution of sample means will approximate a normal distribution, regardless of the population's original distribution shape. As sample size n increases, the sampling distribution of the mean approaches a normal distribution with mean μ and standard error σ/√n. **Key formula:** The standardized score is **z = (x̄ - μ)/(σ/√n)**, where x̄ is the sample mean. This theorem is fundamental because it allows us to make statistical inferences about populations even when we don't know their underlying distribution.