Normal Approximation for the Poisson Distribution Calculator

More about the Poisson distribution probability so you can better use the Poisson calculator above: The Poisson probability is a type of discrete probability distribution that can take random values on the range $[0, +\infty)$.

When the value of the mean $\lambda$ of a random variable $X$ with a Poisson distribution is greater than 5, then $X$ is approximately normally distributed, with mean $\mu = \lambda$ and standard deviation $\sigma = \sqrt{\lambda}$.

A continuity correction needs to be used, so then to better adjust the approximation, so we use:

$$\Pr(a \le X \le b) \approx \Pr(a - \frac{1}{2} \le X_{Normal} \le b + \frac{1}{2} )$$ $$= \Pr \left(\frac{a - \frac{1}{2} - \lambda}{\sqrt{\lambda}} \le Z \le \frac{b + \frac{1}{2} - \lambda}{\sqrt{\lambda}} \right)$$

You can also use our calculator to compute the exact Poisson probabilities .

Other normal approximations

A similar normal approximation is the normal approximation to the binomial distribution , which is actually more widely used than the one for the Poisson distribution.