# normal approximation to binomial and poisson

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?

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