Binomial OR poisson

1. Aug 4, 2004

denian

in a town, one of a hundred occupants loves fishing. what is the minimum occupants must be chosen so that the probability that there is at least one occupant who loves fishing is more than 0.7?

i hope u understand the question, because im doing some direct translation from my language to english.

ok. so, should i use poission or binomial. both lead to a very close answer. but which is more suitable. thx.

2. Aug 4, 2004

Poisson is a suitable approximation to binomial when $$\lambda$$ is small enough and $$n$$ is large enough that $$\left(1-\frac{\lambda}{n}\right)^n\approx e^{-\lambda}$$, $$\frac{n(n-1)\cdots(n-i+1)}{n^i}\approx 1$$ and $$\left(1-\frac{\lambda}{n}\right)^i\approx 1$$. Poisson looks fine for this.

Last edited: Aug 4, 2004
3. Aug 5, 2004