When using a Poisson distribution to approximate a binomial distribution, the standard deviation of the Poisson distribution is np where n is the sample size and p is the probability of an event of interest.

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The standard deviation of a Poisson distribution is the square root of its mean, which is λ (lambda), not np. In a Poisson approximation to a binomial distribution, λ is equal to np.

When Using a Poisson Distribution to Approximate a Binomial Distribution