A LevelMathsAQAStatisticsRevision NotesStatistical DistributionsWorking with DistributionsNormal Approximation of Binomial

Normal Approximation of Binomial (AQA A Level Maths: Statistics): Revision Note

Exam code: 7357

Dan Finlay

Written by: Dan Finlay

Reviewed by: Lucy Kirkham

Updated on

AQA Maths: StatisticsOCR Maths A: Statistics

Normal approximation of a binomial distribution

When can a normal distribution be used to approximate a binomial distribution?

  • A binomial distribution begin mathsize 16px style X tilde straight B left parenthesis n comma p right parenthesis end style can be approximated by a normal distribution begin mathsize 16px style X subscript N tilde straight N left parenthesis mu comma sigma squared right parenthesis end style  provided

    • n is large

    • p is close to 0.5

  • The mean and variance of a binomial distribution can be calculated by:

    • mu equals n p

    • sigma squared equals n p left parenthesis 1 minus p right parenthesis

4-4-2-normal-approximation-of-binomial-diagram-1

Worked Example

The random variable X tilde straight B left parenthesis 1250 comma 0.4 right parenthesis 

(i) Explain why a normal distribution can be used to approximate the distribution of .

 

(ii) Write down the approximating normal distribution.

Answer:

4-4-2-normal-approximation-of-binomial-we-solution-aqa

Examiner Tips and Tricks

  • In the exam, you will only be asked to describe the approximating distribution and not to use it.

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Author
Reviewer
Dan Finlay

Author: Dan Finlay

Expertise: Portfolio Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Lucy Kirkham

Reviewer: Lucy Kirkham

Expertise: Content Creator

Lucy has been a passionate Maths teacher for over 12 years, teaching maths across the UK and abroad helping to engage, interest and develop confidence in the subject at all levels.Working as a Head of Department and then Director of Maths, Lucy has advised schools and academy trusts in both Scotland and the East Midlands, where her role was to support and coach teachers to improve Maths teaching for all.