gen-explain-the-central-limit-theorem-as-you-would-to-a-capable-8f8b

Explain the central limit theorem as you would to a capable student, in 3-4 sentences.

The Central Limit Theorem states that when you take many random samples from *any* population and calculate their means, those sample means will form a normal (bell-shaped) distribution, even if the original population isn't normally distributed. This happens as long as your sample size is large enough (typically n ≥ 30). The distribution of sample means will be centered at the true population mean, and its spread (standard error) will be the population standard deviation divided by the square root of the sample size. This is incredibly powerful because it allows us to make probabilistic statements and conduct hypothesis tests about population means, regardless of the original population's shape.