I was reading about normal approximation to binomial distribution and I dunno how it works for cases when you say for example p is equal to 0.3 where p is probability of success.
On most websites it is written that normal approximation to binomial distribution works well if average is greater than 5. I.e. np> 5 But I am unable to find where did this empirical formula came from?
If n is quite large and probability of success is equal to .5 then i agree that normal approximation to binomial distribution is going to be quite accurate. But what about other cases? How can one say np> 5 is the condition for doing normal approximation?