Binomial and its approximations by Normal and Poisson

Author:
zeimusu
The Binomial distribution can be approximated by the normal distribution and the Poisson distribution. For what values of n and p are these approximations valid. Here n is the number of trials and p is probabiltiy of success in any trial.
If p is small and n is not too small, a Poisson approximation is appropriate. If n is large and p is near 0.5 a normal approximation is appropriate. If p is large, then the problem may be reframed bu considering the number of failures.