The Normal Approximation to the Binomial Distribution

Shows the binomial distribution [math]X \sim \mbox{Bin}(n,p)[/math] and the probability [math]P(X \le r)[/math]. Click the checkbox to show the distribution [math]Y \sim \mbox{N}\left(\mu, \sigma^2 \right)=\mbox{N}(np,npq)[/math], the probability [math]P(Y \le r)[/math] will also be shown. Click continuity corr. to show the continuity correction and the probability [math]P(Y \le r+0.5)[/math] will also be shown.

For what values of [math]p[/math] and [math]n[/math] are the two distributions similar? Why is the continuity correction needed? Created by Dr GJ Daniels