THE CENTRAL LIMIT THEOREM AND THE ROLE OF THE NORMAL DISTRIBUTION IN ITS APPLICATION

This article discusses the mathematical essence of the Central Limit Theorem, the principles of its proof, and its relationship with the normal distribution. The paper analyzes the practical applications of the theorem in economics, engineering, and natural sciences. The importance of the normal distribution in statistical modeling and its role as a universal law in probability theory are highlighted. The research results expand the possibilities of analyzing and predicting real processes using the Central Limit Theorem.