Final answer:
The central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as the sample size increases. It is a fundamental concept in statistics.
Step-by-step explanation:
The central limit theorem (CLT) is a fundamental concept in statistics. It states that when you take a sufficiently large sample size from any population, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. This means that as the sample size increases, the sampling distribution of the means becomes more and more normally distributed.
For example, let's say you have a population of students and you randomly select samples of different sizes from this population. The central limit theorem tells you that as the sample size increases, the distribution of the sample means will approach a normal distribution, even if the population distribution is not normal.
It is important to note that the central limit theorem assumes certain conditions, such as random sampling and independence of observations.