BINOMIAL AND NORMAL DISTRIBUTIONS.

Abstract

Annotation: This article examines the mathematical and conceptual relationship between the binomial distribution and the normal distribution. By exploring the Law of Large Numbers and the Central Limit Theorem, this study demonstrates how the discrete binomial distribution converges toward the continuous normal distribution as the number of independent Bernoulli trials increases. The analysis highlights the conditions for this approximation, specifically focusing on the roles of sample size and success probability, providing a bridge between discrete probability theory and continuous statistical modeling.