The normal distribution is often used as a model in practical situations. When a problem is set in a practical context the first task is to convert the information into the language of the normal distribution. If the variable X is normally distributed with mean \mu and standard deviation \sigma then

\qquad \qquad P(X \le x) = \displaystyle \Phi \left(\frac{x-\mu}{\sigma}\right)

\qquad \qquad P(X \le x) = \displaystyle \Phi \left(\frac{x-\mu}{\sigma}\right)

## Software/Applets used on this page

## Glossary

### mean

the sum of all the members of the list divided by the number of items in the list.

### normal distribution

A key distribution in statistics which is used to model many naturally occurring phenomena, such as heights and weights; its distribution is bell-shaped.

### standard deviation

The square root of the variance; a measure of dispersion.

### union

The union of two sets A and B is the set containing all the elements of A and B.

### variable

A value which is unknown and free to vary, often denoted by x or y.

## This question appears in the following syllabi:

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

AQA A-Level (UK - Pre-2017) | S1 | The Normal Distribution | Probabilities in context | - |

AQA A2 Maths 2017 | Statistics | The Normal Distribution | Probabilities in Context | - |

AQA AS/A2 Maths 2017 | Statistics | The Normal Distribution | Probabilities in Context | - |

CCEA A-Level (NI) | S1 | The Normal Distribution | Probabilities in context | - |

CIE A-Level (UK) | S1 | The Normal Distribution | Probabilities in context | - |

Edexcel A-Level (UK - Pre-2017) | S1 | The Normal Distribution | Probabilities in context | - |

Edexcel A2 Maths 2017 | Statistics | The Normal Distribution | Probabilities in Context | - |

Edexcel AS/A2 Maths 2017 | Statistics | The Normal Distribution | Probabilities in Context | - |

I.B. Higher Level | 5 | The Normal Distribution | Probabilities in context | - |

I.B. Standard Level | 5 | The Normal Distribution | Probabilities in context | - |

Methods (UK) | M15 | The Normal Distribution | Probabilities in context | - |

OCR A-Level (UK - Pre-2017) | S2 | The Normal Distribution | Probabilities in context | - |

OCR A2 Maths 2017 | Statistics | The Normal Distribution | Probabilities in Context | - |

OCR MEI A2 Maths 2017 | Statistics | The Normal Distribution | Probabilities in Context | - |

OCR-MEI A-Level (UK - Pre-2017) | S2 | The Normal Distribution | Probabilities in context | - |

Pre-U A-Level (UK) | Prob | The Normal Distribution | Probabilities in context | - |

Universal (all site questions) | N | The Normal Distribution | Probabilities in context | - |

WJEC A-Level (Wales) | S2 | The Normal Distribution | Probabilities in context | - |