Conditions needed to approximate a Binomial distribution using a Normal distribution? Okay. So, many sources state different conditions for approximating binomial using normal. Variations I've seen are as follows. Assuming that we have Bin(n,p):
1. np and n(1-p) are both large (say, 20 or bigger)
2. large n, p close to 0.5
3. large n, np>9(1-p)
My questions:
1. Are all 3 of these valid? Justify your answer.
2. Is there a set of conditions which can summarise all 3 given above (if they are valid)?
Note: Before any of you say "First, what is your opinion about this?", I personally don't know much about these distributions since I'm studying stats at a basic level. I know quite a few distributions and a bit about pdf's, cdf's, mgf's but not really that much more

The usual conditions are that $n\geq 50$ and both $np$ and $n(1-p)>5$.
Note that if $p$ is close to $0.5$ your third condition is inconsistent with your first condition.
