Normal Approximation to the Binomial Distribution
Let X count the number of successes in n independent Bernoulli trials that each have constant probability p of success. Then, the total number of successes X is a random variable that has a binomial distribution with parameters n and p. The normal distribution with mean np and variance np(1-p) can be used as an approximation to the binomial distribution under certain conditions.
Move the sliders for n and p to change the parameters. Click the checkbox on the right in order to view the normal approximation to the binomial. Click on point A and move the point using the arrows on your keyboard. As you adjust the parameters and move point A, compare the cumulative probability computed with a binomial curve to that computed with a normal curve. For what values of n and p is the normal approximation adequate?