Introduction

In the first tutorial I show you what a Poisson Distribution is by considering various examples. You are then introduced to the formula for calculating the probability of r success and then taken through a typical example.

Tutorial : Introduction to the Poisson Distribution

Changing the Mean + Cumulative Probability Tables

In this tutorial I show you how to handle the mean changing over a period of time or space. You are also introduced to using the Cumulative Poisson Distribution Probability tables.

The following example is used which you may like to try before looking at the tutorial and worked solution.

In a certain factory accidents occur at a mean rate of 2 per week. Assuming the number of accidents per week follows a Poisson Distribution, find the probability of less than 3 accidents occuring in a given fortnight.

Tutorial : Changing the Mean / Introduction to the Cumulative Probability Tables

Calculating an observed value using Tables

You maybe asked to find an observed value as in the following question.

A shop sells a particular T.V at a mean rate of 5 per day. Assuming that the number sold per day follows a Poisson distribution. Find the smallest number of T.V.'s that must be in stock at the beginning of the day in order to have at least a 99% chance of being able to meet all demands that day.

Try it as part of your revision on the Poisson distribution but if stuck look at the tutorial below.

Tutorial on using the Cumulative tables and calculating x

Poisson Approximation to the Binomial Distribuition

The Poisson distribution can be used as an approximation to the Binomial distribution providing certain conditions are met. This can greatly simplify calculations.

In the next tutorial you are shown these conditions.

Tutorial on the Poisson approximation to the Binomial distribution

Now we have an example where the approximation can be used. However, the video will compare the real answer with the approximation. You may like to try it before looking at the video and comparing your working.

A factory produces a particular electrical component and on average 1 in 50 is faulty. In a batch of 300 components taken at random, what is the probability of having at least eight faulty components?

Worked solution comparing the exact and approximate probabilities.