The Poisson distribution may also be used to find approximate binomial probabilities when n is large and p is small, by letting μ be np. This method provides for faster calculations of probabilities...

The Poisson distribution may also be used to find approximate binomial probabilities when n is large and p is small, by letting μ be np. This method provides for faster calculations of probabilities of rare events such as exotic diseases. For example, assume the incidence rate (proportion in the population) of a certain blood disease is known to be 1%. The probability of getting exactly seven cases in a random sample of 500, where μ = np = (0:01)(500) = 5, is

P(Y = 7)=(5⁷e
^-5)∕7! = 0:1044:

Suppose the incidence of another blood disease is 0.015. What is the probability of getting no occurrences of the disease in a random sample of 200? (Remember that 0! = 1.)