Question

ch 15 as the sample size increases, the distribution of $\bar{x}$(sample mean) changes shape: it looks less like that of the population and more like a normal distribution. when the sample is large enough, the distribution of $\bar{x}$(sample mean) is very close to normal. this is true no matter what shape the population distribution has, as long as the population has a finite standard deviation $sigma$. this famous fact of probability theory is called the:
○ law of large numbers.
○ distributive theorem
○ normal theorem
● central limit theorem

Explanation:

The central limit theorem states that as sample size increases, the sampling - distribution of the sample mean approaches a normal distribution, regardless of the population's distribution shape, given a finite population standard deviation. The law of large numbers is about the convergence of the sample mean to the population mean. There is no "distributive theorem" or "normal theorem" in this context.

Answer:

central limit theorem