Use this display to compare the Binomial and Poisson distributions. What values of n and p make them similar?

## Summary/Background

For large n and small p, the Poisson distribution gives a good approximation to the Binomial distribution.

## Software/Applets used on this page

Copyright © R F Barrow, 2000-2003 Waldomaths

## Glossary

### binomial distribution

A statistical situation where there are only two mutually exclusive outcomes, whose probabilities of occurring are constant.

### poisson distribution

A distribution used to estimate probabilities of random events which have a small probability of occuring, for example volcanic eruptions, accident rates.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S3 | The Poisson Distribution | Approximation to the Binomial | - |

AQA AS Further Maths 2017 | Statistics | Poisson Distribution | Poisson as Approximation to Binomial | - |

AQA AS/A2 Further Maths 2017 | Statistics | Poisson Distribution | Poisson as Approximation to Binomial | - |

CCEA A-Level (NI) | S1 | The Poisson Distribution | Approximation to the Binomial | - |

CIE A-Level (UK) | S2 | The Poisson Distribution | Approximation to the Binomial | - |

Edexcel A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | Approximation to the Binomial | - |

Edexcel AS Further Maths 2017 | Further Statistics 1 | Poisson Distributions | Poisson as Approximation to Binomial | - |

Edexcel AS/A2 Further Maths 2017 | Further Statistics 1 | Poisson Distributions | Poisson as Approximation to Binomial | - |

I.B. Higher Level | 7 | The Poisson Distribution | Approximation to the Binomial | - |

Methods (UK) | M15 | The Poisson Distribution | Approximation to the Binomial | - |

OCR A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | Approximation to the Binomial | - |

OCR AS Further Maths 2017 | Statistics | Poisson Distribution | Poisson as Approximation to Binomial - Extra | - |

OCR MEI AS Further Maths 2017 | Statistics A | Poisson Distribution | Poisson as Approximation to Binomial - Extra | - |

OCR-MEI A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | Approximation to the Binomial | - |

Universal (all site questions) | P | The Poisson Distribution | Approximation to the Binomial | - |

WJEC A-Level (Wales) | S1 | The Poisson Distribution | Approximation to the Binomial | - |