5. Sampling Distributions

The Central Limit Theorem — Quiz

Test your understanding of the central limit theorem with 5 practice questions.

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Practice Questions

Question 1

What does the Central Limit Theorem say about the sampling distribution of the sample mean when the sample size is large enough?

Question 2

If the population has mean $\mu=50$ and standard deviation $\sigma=10$, what is the mean of the sampling distribution of $\bar{x}$?

Question 3

If the population has standard deviation $\sigma=12$ and the sample size is $n=36$, what is the standard deviation of the sampling distribution of $\bar{x}$?

Question 4

Why does the sampling distribution of $\bar{x}$ usually become less spread out as sample size increases?

Question 5

Which statement best describes the effect of the Central Limit Theorem on the shape of the sampling distribution of $\bar{x}$?