My lecturer said that the following approximations are best when

  • normal approximation to the binomial is best when np$\ge$5 and n(1-p)$\ge$5
  • normal approximation to the poisson when $\lambda$>20
  • poisson approximation to the binomial when n is large(>50) and p is small(<0.1)

But when I searched for these approximations there were different conditions used.As these are rule of thumb only these can change.But I want to know if these given conditions are correct and in a situation where binomial can be approximated by both normal and poisson what should be used?For instance in a hypothesis testing if data are binomially distributed with sample size is 200 and p=0.03 should this be approximated by normal or poisson?

  • $\begingroup$ Nothing wrong with asking here, but there is a statistics site in the stackexchange network that might be better for you. $\endgroup$ Oct 4, 2013 at 12:42
  • $\begingroup$ "when I searched for these approximations there were different conditions used" Which conditions? $\endgroup$
    – Did
    Oct 4, 2013 at 12:45

1 Answer 1


The thing with approximations is that there is no hard and fast answer. There's no fixed rule as to what constitutes a large sample size or a small probability. For this course, I'd advise following your lecturer's guidance, but be aware of the fact that the notions of large and small are entirely arbitrary and subjective.

As for what to do in the situation where both poisson and normal approximations are valid, I'd advise asking your lecturer about that. Personally, I'd use both, since if the hypothesis is valid for one it should be valid for the other.

  • $\begingroup$ Thank you for your explanation $\endgroup$
    – clarkson
    Oct 5, 2013 at 4:02

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