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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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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