The Central Limit Theorem states that regardless of the shape of a population, the distributions of sample means are normal if sample sizes are large.
If samples of size n are drawn randomly from a population that has a mean of μ and a standard deviation of σ, the sample means are approximately normally distributed for sufficiently large sample sizes (n ≥ 30) regardless of the shape of the population distribution. If the population is normally distributed, the sample means are normally distributed for any size sample.
Central Limit Theorem
Introduction to the central limit theorem and the sampling distribution of the mean
The Central Limit Theorem, Part 1 of 2
The Central Limit Theorem, Part 2 of 2
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