Question

For a binomial random variable X, if np and n(1-p) are both at least 5 what can we do?

Answer 1

For a binomial random variable, if we find that both np and n(1-p) are at least 5, then we can perform the

Normal Approximation to Binomial Distribution.

We usually use this when n is very large, and p is small; but a Poisson distribution cannot be applied because of the fact that the np value is not small enough. That is the ideal case to use normal Approximation to Binomial Distribution; in which we actually calculate the mean and standard deviation according to the binomial formula, but use the random variable as Normal.

So, the answer is, we can do Normal Approximation to Binomial Distribution.