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The Rule of five:
The normal with means np and npq can be used to approximate the binomial distribution with parameters n and p if
Here,
Normal approximation cannot be used for the binomial distribution with
The direct approximation of the binomial by Poisson says that the binomial distribution with parameters n and p has the same distribution as the Poisson with the parameter np when np is large.
The value of np is obtained as shown below:
Since the value of n is large and p is small and the value of np is small, the binomial distribution can be approximated to Poisson.
That is, the binomial distribution with