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A LevelMaths: StatisticsAQARevision Notes4. Statistical Distributions4.4 Choosing Distributions (A Level only)4.4.2 Normal Approximation of Binomial

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

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Normal Approximation of Binomial

When can I use a normal distribution 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.

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

Examiner Tip

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

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    Dan

    Author: Dan

    Expertise: Maths

    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.