When Is the Binomial Distribution Well Approximated by the Poisson?

In which of the following situation the Poisson distribution can be good approximation of the binomial distribution?

The Poisson distribution occurs in several important situations. It is the limit of the binomial distribution b ( x ; n , p ) when one lets n → ∞ and p → 0 in such a way that remains fixed at the value . In practice, the Poisson distribution is an adequate approximation to the binomial distribution if n ≥ 1 0 0 and.

How well does the Poisson estimate the binomial distribution?

The result is very close to the result obtained above dpois(x = 1, lambda = 1) =0.3678794. The appropriate Poisson distribution is the one whose mean is the same as that of the binomial distribution; that is, λ=np, which in our example is λ=100×0.01=1.