In this section we consider normal approximation to the binomial and Poisson distributions. We will be referring to the two notions of accuracy of an approximation in Lab 3. (Refer to items (a) and (b) in section II in Lab 3).

Normal approximation to the binomial distribution

Set , where is the pth quantile of the binomial distribution with parameters and n and i take on only integer values. Start with n = 100. If n is increased by steps of size 100, how large does n have to be so that normal approximation to the binomial distribution with parameters n and is accurate in the sense of (a) when we take ? Next, increasing n by steps of size 5, how large do we have to make n in order that the approximation is accurate in the sense of (b), again setting ? Try few values close to the value you have just found, and check if the approximation in the sense of (b) still hold.

Normal approximation to the Poisson distribution

Set where is the pth quantile of the Poisson distribution with parameter and i takes on only integer values. If is increased by steps of size 50, how large do we have to make in order that the normal approximation to the Poisson distribution with parameter is accurate in the sense of (a), where we set for a given ? Next, increasing by steps of size 5, how large does have to be so that the approximation is accurate in the sense of (b)? Start with .