Statistical Applets Normal Approximation to Binomial Distributions

The Central Limit Theorem says that as n increases, the binomial distribution with n trials and probability p of success gets closer and closer to a normal distribution. That is, the binomial probability of any event gets closer and closer to the normal probability of the same event. The normal distribution has the same mean μ = np and standard deviation σ = √np(1-p) as the binomial distribution.	You can use the sliders to change both n and p. Click and drag a slider with the mouse. Start by choosing p. The binomial distributions are symmetric for p = 0.5. They become more skewed as p moves away from 0.5. The bars show the binomial probabilities. The vertical gray line marks the mean np. The red curve is the normal density curve with the same mean and standard deviation as the binomial distribution. As you increase n, the binomial probability histogram looks more and more like the normal curve.

Statistical Applets

Normal Approximation to Binomial Distributions

The Central Limit Theorem says that as n increases, the binomial distribution with n trials and probability p of success gets closer and closer to a normal distribution. That is, the binomial probability of any event gets closer and closer to the normal probability of the same event. The normal distribution has the same mean μ = np and standard deviation σ = √np(1-p) as the binomial distribution.

You can use the sliders to change both n and p. Click and drag a slider with the mouse. Start by choosing p. The binomial distributions are symmetric for p = 0.5. They become more skewed as p moves away from 0.5. The bars show the binomial probabilities. The vertical gray line marks the mean np. The red curve is the normal density curve with the same mean and standard deviation as the binomial distribution. As you increase n, the binomial probability histogram looks more and more like the normal curve.