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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

More Lessons for Statistics

Math Worksheets

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

Introduction to the central limit theorem and the sampling distribution of the mean

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