3.5 The normal distribution

Students should be able to recognise that many things closely follow a Normal Distribution, eg heights of people, size of things produced by machines, errors in measurements, blood pressure, marks on a test etc. In these and similar situations, a graph of the distribution will have a ‘bell’ shaped curve.

S1 Properties of the normal distribution



Additional information


knowledge that this is a symmetrical distribution and that the area underneath the normal ‘bell’ shaped curve represents probability

knowledge that approximately of observations lie within 1 standard deviation of the mean and that approximately of observations lie within 2 standard deviations of the mean

S2 Notation



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use of the notation to describe a normal distribution in terms of mean and standard deviation

use of the notation for the standardised normal distribution with mean = 0 and standard deviation = 1

S3 Calculating probabilities



Additional information


using a calculator or tables to find probabilities for normally distributed data with known mean and standard deviation

the finding of an unknown mean or standard deviation by making use of percentage points will not be required