As explained in chapter 03, (a)The Poisson distribution provides a very good approximation to the binomial when n is large and θ is small. (b) Normal distribution provides good approximations to binomial (n,θ) My query is when do we use poisson to approximate the binomial distriibution and when do we use normal distribution to the binomial distriibution ? The solution of Q2.16 of Q&A bank uses central limit theorem to approximate the binomial distribution, but does not use continuty correction.I think the solution should take the factor of 0.5 as we are approximating a discrete distribution with a continous distribution.
Well - try the normal approximation first (if np>5 and nq>5 then it's good). If it's not appropriate then use a Poisson approximation instead. Here we're approximating a compound binomial. A compound binomial has a mixed distribution (it's continuous for P(S>0) and is discrete for P(S=0)). Since it's mostly continuous a continuity correction is not appropriate.
The setup of test statistics and the range of a confidence intervals seem a little easier under normal approximation to binomial (if possible). I think CI's using direct binomial for is long compared.
