This distribution is used quite frequently in reliability analysis. It can be considered an extension of the binomial distribution when n is infinite. It can be used to approximate the binomial distribution when n > 20 and p < 0.05.
If events are Poisson distributed, they occur at a constant average rate and the number of events occurring in any time interval are independent of the number of events occurring in any other time interval. For example, the number of failures in a given time would be given by: