The Normal Approximation to the Binomial Distribution

Binomial distribution is determined by n (number of trials) and p (the probability of success)

The normal distribution is often used to solve problems that involve the binomial distribution since when n is large (say 100), the calculations are too difficult to do by hand using the binomial distribution. When p is approximately 0.5 and as n increases, the shape of the binomial distribution become similar to the normal distribution. The larger the n and the close p is to.5 the more similar shape of the binomial distribution is to the normal distribution.

However, when p is close to 0 or 1 and n is
relatively small, the normal approximation is inaccurate.

Remember:
Normal approximation should be used only when n . p and n . q are both greater than 5.

J. Santillan