A national survey by Gallup interviewed 1014 adults and found that they had consumed, on average, 4.2 alcoholic beverages in the past seven days. Considering a sample of 1014 adults to be a large sample, which of the following statements is TRUE?

Question

Quizplus · Accepted Answer

By the central limit theorem, the average of repeated samples of size 1014 is approximately normally distributed, regardless of the underlying distribution of the population. The central limit theorem doesn't state that an individual sample is normally distributed. Therefore, options A and C are incorrect. Option D is partially correct, as the law of large numbers confirms that the sample average will converge to the population average as the sample size increases, but it does not imply that the sample average is normally distributed.

A National Survey by Gallup Interviewed 1014 Adults and Found