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,

is approximately N(0,1)

(a)
X<280 和 的意思是一樣的, 在連續較正項之下

(b)