AS/A2 Stats 1 Stats 3

S2 Topic 1: Binomial and Poisson distributions
Poisson approximation to the Binomial distribution
The Poisson distribution can be used as an approximation to the Binomial distribution. Choose values for n and p to represent the binomial distribution B(n,p). Press Compute. The Poisson distribution P(l), where l= np, will be used to calculate the probabilities P(X=x), for values of x from 0 to 59. The Binomial probabilities are also displayed so that comparisons can be made. For what values of n and p do you get a good match?

n 7 10 12 50 52 100 120 160 170	p
l =

x	Poisson P(X=x)	Binomial P(X=x)	% Error

Summary For large n and small p, the Poisson distribution gives a good approximation to the Binomial distribution. Note that in the above display a large % error may occur when the values of the probabilities are themselves very small indeed. © MathsNet 2001