Question

when is the binomial distribution well approximated by the poisson

Answer 1

The Binomial distribution can be approximated well by Poisson when n is large and p is small with np < 10, as stated above. This is true because \lim_{n \rightarrow \infty}

{n \choose x} p^x(1-p)^{n-x}=\frac{\lambda^x e^{-\lambda}}{x!} , where λ = np. Here is an example. Suppose 2\% of a certain population have Type AB blood.