Why normal approximation to binomial distribution uses np> 5 as a condition 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?

For $np$ and $nq$ to increase $n$ must increase. $n$ is the number of independent trials, so it should be clear that the more independent trials made, the more accurate your approximation is.  The probability histogram approximates a normal curve pretty accurately when $np$ and $nq$ are greater(or equal to) $5$.  However bigger is better!  If $np$ and $nq$ were greater than $10$ the probability histogram would approximate the normal curve even more.
