Please type the assumptions required for a binomial normal a

Please type the assumptions required for a binomial normal approximation using inequalities and the following symbols (n,p,q) where n is the sample size, p is the probability parameter from the binomial experiment, and q=(1-p).

(write both answers together separated by a single space).

Solution

let X~Bin(n,p)

then E[X]=np

V[X]=npq

now the assumption for which a binomial distribution can be approximated as a normal distribution is-

n=sample size has to be very large enough that is n should tensed infinity.

then (X-np)/sqrt(npq)~N(0,1) approximately.