Can a Binomial Distribution be standardized to a Standard Normal distribution? Using Central Limit Theorem..
2026-04-01 15:40:42.1775058042
Can a Binomial Distribution be standardized to a Standard Normal distribution?
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Any normal distribution can be transformed to the standard normal distribution by means of the mapping $ z = \frac{x - \mu}{\sigma}$. We know that a binomial distribution with parameters $n$ and $p$ (representing number of trials and success probability, respectively) can be approximated by a normal distribution with mean $np$ and variance $np(1-p)$. Applying the standardization above gives a standard normal distribution.
As Kenny Wong states, I should add that $n$ should be "large enough" in order for the approximation to be good. He claims $n$ needs to be at least $10$, while I found that in many texts, $n \geq 30$ is usually the way to go. I don't think this magic number is uniform, but the idea is to make sure you have enough sample points.