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). [br][br]It should be evident that:[br][br]If [math]X\sim B\left(n,p\right)[/math] and n is sufficiently large then the distribution of X is approximately normal. [br][br]If p is close to 0 or 1, then n must be larger than if p is closer to [math]\frac{1}{2}[/math]. [br][br]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. [br][br]The requirement for np>5 [u]and[/u] nq>5 is a common condition for using the the normal distribution to approximate the binomial distribution.[br][br][br][br]