Question

If the a binomial distribution B(n=300, p=0.05) is approximated by a normal distribution, what are the values of all parameters of this normal distribution? And what is the condition that this approximation is applicable?

Answer 1

The condition for approximated normal is np ≥ 5   and n(1 − p) ≥ 5

we have np=300*0.05=15≥5 and n(1-p)=300*(1-0.05)=285 ≥ 5 so our condition for approximation is satisfied

now if X~B(n,p) than it will be approximated by X~N(np,np(1-p)) so hers X~N(15,14.25) so the paremeters for approximated normal is and