As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.

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21-10-2022
Mathematics

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As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.

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Qwtiger Qwtiger · Answer 1 · 2022-10-26T14:11:12-04:00

As the sample size becomes larger, the sampling distribution of the sample mean approaches a normal distribution.

In the theory of probability, the central limit theorem states that the distribution of a sample mean approximates a normal distribution as the size of the sample increases. For the central limit theorem to hold, it is necessary that the sample size at least cross a margin of 30. Having a sufficiently larger sample size can predict the characteristics of the sample more accurately. The central limit theorem is applicable when we are analyzing large data sets.