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

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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 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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