MathsNet: N - The Normal Distribution

Page ID: 2422

N | The Normal Distribution | Probabilities in context | «Heights»

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)

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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.

Full Glossary List

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	-