According to the central limit theorem, what can be said about samples taken from any distribution?

The central limit theorem is a fundamental statistical principle that states that regardless of the original distribution of a population, the distribution of the sample means will approach a normal distribution as the sample size increases, typically when the sample size is 30 or more. This phenomenon occurs even when the population itself is not normally distributed.

As the sample size grows, the variability of the sample means decreases, leading to the formation of a bell-shaped curve that characterizes the normal distribution. This theorem is critical in the field of statistics because it allows for making inferences about population parameters using sample data, assuming the sample size is adequate.

In contrast, the other options do not hold true in relation to the central limit theorem. Samples taken from any distribution do not necessarily yield a uniform, binomial, or skewed distribution, especially as the size of the samples increases. Instead, it is the convergence towards a normal distribution that is the key takeaway from this theorem.