Minimum Occupants for Probability of Fishing > 0.7

[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 I am 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.

 

[grady]

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.

 

[denian]

thank you, grady