Question

Under what conditions does the binomial distribution tend to normal distribution?

Answer 1

Answer:

  The Binomial distribution will tend towards the normal distribution because of the Central Limit Theorem for Sum.

  A binomial distribution is equivalent to the sum of  n  iid Bernoulli random  variables with parameter  p .

  The less skewed the distribution, the sooner it will approach the normal  distribution when you take an independent sum. If  p  is close to 0.5, you   can usually approximate the Binomial with a Normal distribution for fairly   small  n  (let’s say 30 or less). If  p  is close to 0 or 1, then you will need larger values of  n  in order to get a good approximation in some cases.