Approximation

Poisson Distribution

Hypergeometric Distribution

Normal Distribution

De Moivre-Laplace theorem

Suppose Binomial(n,p)\text{Binomial}(n,p), when np(1−p)>5np(1-p)\gt 5, normal distribution N(np,np(1−p))\mathcal{N}(np, np(1-p)) provides a good approximation of Binomial(n,p)\text{Binomial}(n,p).