State the Central Limit Theorem in one sentence.

• A. The sampling distribution of the mean becomes approximately normal as sample size grows, regardless of population shape.
• B. The distribution of the population mean becomes normal as sample size grows.
• C. The sample mean becomes normal regardless of the sample size.
• D. The sampling distribution of the variance becomes normal with large sample.

Answer: (A)

The idea being tested is that the averages from many random samples form a distribution that becomes normal as the sample size grows, even if the underlying population is not normal. This is about the sampling distribution of the mean, not the population itself, and as n increases that distribution centers at the true population mean with spread equal to the population standard deviation divided by the square root of n. That’s why the statement describing the sampling distribution of the mean becoming approximately normal with large sample size, regardless of population shape, is the best answer. The other choices mix up what becomes normal (the population distribution, or the mean for all sample sizes) or focus on variance instead of the mean.