The normal approximation to the binomial applies when n is large and the success probability p is not too close to 0 or 1. The binomial probability of is approximated by the normal probability of .
When np and n(1-p) are both large, say, greater than 15, the binomial distribution is well approximated by the normal distribution having and . That is,
假設隨機變數 X 為 1000 位成年人中長期飲運含有酒精成份飲料的人數. 則在所占比例 30% 的假設下, X 為 n=1000,p=.3 的二項分配, 也就是說 , 因此
意思是說 X 的分配趨近於 N(300,14.49).