Approximating a Binomial Distribution using a Normal Distribution (2.04d, 2.04h)
- Binomial Distribution
The applet can be used to examine when it is reasonable to use a normal distribution as a good model to approximate a binomial distribution by plotting the frequency distribution as a histogram and plot and then comparing it with a normal distribution with the same mean and variance (mean=np and variance=npq). It should be evident that: If and n is sufficiently large then the distribution of X is approximately normal. If p is close to 0 or 1, then n must be larger than if p is closer to . Showing a 2nd distribution with p'=1-p and with the same value of n (use the check box (Set n=n') to lock this) is useful when exploring the idea that if p is closer to 0 or 1 then n must be larger. The requirement for np>5 and nq>5 is a common condition for using the the normal distribution to approximate the binomial distribution.