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.