Chicken and egg

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

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Overview of task

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

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Strand

Statistics

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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.

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Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson / Edexcel

•OCR

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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.

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Resources/documentation

There is a PowerPoint presentation and interactive whiteboard resources.

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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.

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Possible extensions

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

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Acknowledgement

Developed by Derek Robinson for the CMSP.