The Central Limit Theorem states that the distribution of the sample mean of a large number of independent, identically distributed random variables will be approximately normally distributed, regardless of the shape of the original distribution. This theorem is a fundamental concept in statistics and is widely used in hypothesis testing and confidence intervals. For example, if we take multiple samples from a population with any distribution, the means of those samples will form a normal distribution. This allows us to make inferences about the population mean even if we don't know the population distribution. The Central Limit Theorem is important because it allows us to make valid statistical inferences, even when our data may not meet the assumption of normality. It is the basis for many statistical methods and plays a crucial role in the field of statistics. Understanding this theorem can help us interpret data more accurately and make informed decisions based on statistical analysis.