
Answer-first summary for fast verification
Answer: Indicates that the sample mean serves as a consistent estimator of the population mean.
**Explanation:** The central limit theorem (CLT) is a fundamental concept in statistics. It states that the distribution of the sample mean will approximate a normal distribution as the sample size increases, regardless of the population's distribution (provided the population has finite variance). - **Option A** is incorrect because the CLT does not require the population to be normally distributed. It applies to populations with any distribution, as long as the sample size is sufficiently large. - **Option B** is correct because the CLT implies that the sample mean is a consistent estimator of the population mean. As the sample size grows, the standard error of the sample mean decreases, and the sampling distribution becomes more concentrated around the population mean. - **Option C** is incorrect because the CLT pertains to the sum (or mean) of independent random variables, not their product. The sum of a large number of independent random variables will approximate a normal distribution under the CLT.
Author: LeetQuiz Editorial Team
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The central limit theorem:
A
Assumes that the population must be approximately normally distributed.
B
Indicates that the sample mean serves as a consistent estimator of the population mean.
C
Asserts that the product of independent random variables follows a normal distribution.
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