What happens to the shape of a sampling distribution of sample means as the sample size n increases Quizizz?

Regardless of the distribution of the population, as the sample size is increased the shape of the sampling distribution of the sample mean becomes increasingly bell-shaped, centered on the population mean.

From the Central Limit Theorem, we know that as n gets larger and larger, the sample means follow a normal distribution. The larger n gets, the smaller the standard deviation of the sampling distribution gets.

In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

The Shape of the Sample Mean Distribution is Normal! The sample mean distribution is a heap shaped, as in the shape of the normal distribution, and centered on the population mean. If the sample size is 30 or more, then the sample means are NORMALLY distributed even when the underlying data is NOT normally distributed!