# Poisson Approximation to the Binomial Distribution

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What are the conditions for which a Poisson Distribution can be used as an approximation to the Binomial distribution?
The binomial distribution tends towards the Poisson distribution when n → ∞ , p → 0 and λ = np stays constant.

Poisson approximation to the Binomial Distribution
This is the 6th in a series of tutorials for the Binomial Distribution.
This tutorial shows you the conditions for which a Poisson Distribution can be used as an approximation to the Binomial distribution by comparing probability graphs of the distributions

Poisson Approximation to the Binomial Distribution (Example)
This is the 6th in a series of tutorials for the Poisson Distribution.
This tutorial runs through an example comparing the actual value to the approximated value and compare the two methods of working.

Poisson approximation to Binomial: S2 Edexcel January 2013 Q1

1. (a) Write down the conditions under which the Poisson distribution can be used as an approximation to the binomial distribution.
The probability of any one letter being delivered to the wrong house is 0.01
On a randomly selected day Peter delivers 1000 letters.
(b) Using a Poisson approximation, find the probability that Peter delivers at least 4 letters to the wrong house.

The Relationship Between the Binomial and Poisson Distributions
A look at the relationship between the binomial and Poisson distributions (roughly, that the Poisson distribution approximates the binomial for large n and small p). This video works through some calculations in an example, showing that the approximate probability from the Poisson can be quite close to the exact probability from the binomial distribution.
(The example used involves albinism. Albinism affects all races, but the rates of albinism vary a little around the world. In Europe and North America, roughly 1 in 20,000 people have some form of albinism).

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