Normal Approximation to Binomial Distribution - Visual Guide #3235541 (License: Personal Use)

This plot compares a binomial probability mass function (PMF) with parameters n=6 and p=0.5-shown as light blue bars at integer k values from 0 to 6-to a continuous normal probability density function (PDF) fitted to the same mean (μ = np = 3) and variance (σ² = np(1-p) = 1.5). The close alignment illustrates when the normal approximation is appropriate for discrete binomial outcomes. Continuity correction can further improve accuracy near boundaries.

Used in statistics education, data science tutorials, and probability reference pages to explain the Central Limit Theorem’s application to binomial distributions; targets learners seeking intuitive understanding of approximation techniques.