Poisson approximation of binomial probabilities

This is yet another experiment to see how good is the approximation of binomial probability when we use Poisson and normal distributions for scenarios with large $n$, and $p$ close to zero or one.

Consider a problem where the random variable $X$ follows a binomial distribution with a known probability of success $p$, and number of trials $n$. If $n$ becomes large, it may not be possible to calculate the probabilities by hand calculation or using a calculator.

We can approximate the binomial distribution with a normal distribution or a Poisson distribution.

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