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?