The Central Limit Theorem (CLT) is one of the most fundamental and powerful results in probability theory and statistics. It explains the behavior of the sampling distribution of the sample mean when random samples are drawn from a population. The theorem states that if a sufficiently large number of independent and identically distributed random samples are taken from any population with a finite mean and finite variance, then the distribution of the sample mean approaches a normal distribution, regardless of the shape of the original population distribution. This remarkable property makes the normal distribution central to statistical analysis and inference. Mathematically, suppose a population has mean ( \mu ) and variance ( \sigma^2 ). If random samples of size ( n ) are selected independently, then the sampling distribution of the sample mean ( \bar{X} ) has mean ( \mu ) and variance ( \sigma^2/n ). As the sample size increases, the standardized variable [ Z=\frac{\bar{X}-\mu}{\sigma/\sqrt{n}} ] approaches the standard normal distribution. In practical applications, a sample size of 30 or more is often considered sufficient, although the required size depends on the shape of the population distribution. Highly skewed populations may require larger samples before the approximation becomes accurate. The theorem relies on certain assumptions. The observations should be selected randomly and independently. The population should have a finite mean and finite variance. When sampling without replacement from a finite population, the sample size should be small relative to the population unless appropriate finite population corrections are applied. These assumptions ensure that the sampling distribution behaves as predicted by the theorem. The significance of the Central Limit Theorem in statistical inference is enormous because it provides the theoretical basis for making conclusions about population characteristics using sample data. Statistical inference involves estimating unknown population parameters and testing hypotheses based on sample observations. Since the exact population distribution is often unknown or difficult to determine, the CLT allows statisticians to use the normal distribution as an approximation for the sampling distribution of the sample mean. One