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StatisticsInferential Statistics

What Is the Central Limit Theorem for Sample Means?

What is the central limit theorem? Explain the sampling distribution of means, its standard error, finite-variance conditions, and sample-size limits.

Question

What does the central limit theorem state with regard to the distribution of sample means?

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Evidence boundary

This answers OpenStax Practice Test 2, question 67. The displayed theorem uses the classical independent, identically distributed, finite-variance assumptions. Normal notation explicitly uses variance as its second parameter; no fixed sample-size threshold guarantees accuracy.