When to approximate Binomial with Poisson and when with Normal?
My Schaum's outline gives the following criteria for deciding when to approximate a binomial distribution with a Poisson or a Normal distribution:
Poisson: 3 requirements:
(1.) n >> p
(2.) np < 5
(3.) n > 50
(1.) n >> p
(2.) np > 5
At first, I thought these guidelines might help me sort out the two cases, because Schaum's says np < 5 for Poisson and np > 5 for Normal, but I've stumbled on a number of exceptions. People will sometimes use Poisson, even though np > 5, provided n is bigger than p by, say, a factor of 10^9.
But I cannot find a consistent pattern here. People eyeball the distribution and make a decision, but I don't have the hang of it yet.
I don't think they will ask you to transform a binomial into a poisson. But generally, if they want you to use a normal approximation, they will ask for the "approximate" probability of x occuring; I suppose, you can say, that, if your n is large enough and your P is very small, and you are not told to approximate, you can use the poisson approximation. The key is whether they are asking for an approximate probability!
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