AQA Certificate Level 3 Mathematical Studies₁₃₅₀

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

	Content	Additional information
S1.1	knowledge that this is a symmetrical distribution and that the area underneath the normal ‘bell’ shaped curve represents probability	knowledge that approximately $\frac{2}{3}$ of observations lie within 1 standard deviation of the mean and that approximately $95 %$ of observations lie within 2 standard deviations of the mean

S2 Notation

	Content	Additional information
S2.1	use of the notation $N (μ, σ^{2})$ to describe a normal distribution in terms of mean and standard deviation	use of the notation $N (0, 1)$ for the standardised normal distribution with mean = 0 and standard deviation = 1

S3 Calculating probabilities

	Content	Additional information
S3.1	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

3.4 Critical analysis of given data and models (including spreadsheets and tabular data)

3.6 Probabilities and estimation

Content

Additional information

S1.1

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

knowledge that approximately $\frac{2}{3}$ of observations lie within 1 standard deviation of the mean and that approximately $95 %$ of observations lie within 2 standard deviations of the mean

Content

Additional information

S2.1

use of the notation $N (μ, σ^{2})$ to describe a normal distribution in terms of mean and standard deviation

use of the notation $N (0, 1)$ for the standardised normal distribution with mean = 0 and standard deviation = 1

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AQA Certificate Level 3 Mathematical Studies₁₃₅₀

3.5 The normal distribution

S1 Properties of the normal distribution

S2 Notation

S3 Calculating probabilities