Question

As the sample size increases, the distribution of sample averages approaches a Normal distribution regardless of the shape of the sampled population. This is identified in which of the following?

A) Assignable variation
B) Type I errors
C) Central limit theorem
D) Mean charts
E) Random variation

Answer 1

The described phenomenon where the distribution of sample averages approaches a normal distribution as sample size grows is known as the Central Limit Theorem.

Step-by-step explanation:

The phenomenon that you're describing is identified by the Central Limit Theorem. In this theorem, it states that as the sample size increases, the distribution of sample means will approach a normal distribution regardless of the population's original distribution, given that the sample size is sufficiently large. It also asserts that the mean of the sample means will be equal to the population mean, and the standard deviation of these sample means, known as the standard error of the mean, is calculated by dividing the population's standard deviation by the square root of the sample size (n).

The correct answer to your question is thus C) Central Limit Theorem.