This is linked to the Baby boom task and a development of it to standardising Normal distributions.

Overview of task

This is linked to the Baby boom task and a development of it to standardising Normal distributions.

Strand

Statistics

Prior knowledge

Students need to be familiar with the statistics: mean, variance and standard deviation and estimating areas under the Normal distribution using tables (and calculators). It would also be useful if students had done work on transforming functions.

Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

Suggested approaches

This is a whole class task with opportunity for group investigation, as it starts with a problem about how to determine the probability for X~N(μ,σ^2) using Z~N(0,1). This should lead to the standard transformation z=(x-μ)/σ and can be linked to the general transformation of functions that students may have met in work on algebra and graphs.

Resources/documentation

There is a PowerPoint presentation and interactive whiteboard resources.

Relevant digital technologies

You could introduce the use of calculators with appropriate statistical functionality to determine areas under Normal distributions, including the Geogebra probability distribution calculator.

Possible extensions

Investigate how the Normal distribution is used in product control in manufacturing.

Acknowledgement

Developed by Derek Robinson for the CMSP.

Materials