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Binomial OR poisson

  1. Aug 4, 2004 #1
    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. jcsd
  3. Aug 4, 2004 #2
    Poisson is a suitable approximation to binomial when [tex]\lambda[/tex] is small enough and [tex]n[/tex] is large enough that [tex]\left(1-\frac{\lambda}{n}\right)^n\approx e^{-\lambda}[/tex], [tex]\frac{n(n-1)\cdots(n-i+1)}{n^i}\approx 1[/tex] and [tex]\left(1-\frac{\lambda}{n}\right)^i\approx 1[/tex]. Poisson looks fine for this.
    Last edited: Aug 4, 2004
  4. Aug 5, 2004 #3
    thank you, grady
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