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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Dan

Last updated

21 October 2023

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Normal Approximation of Binomial

When can I use a normal distribution to approximate a binomial distribution?

A binomial distribution $X ~ B (n, p)$ can be approximated by a normal distribution $X_{N} ~ N (μ, σ^{2})$ provided
- n is large
- p is close to 0.5
The mean and variance of a binomial distribution can be calculated by:
- $μ = n p$
- $σ^{2} = n p (1 - p)$

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

Worked example

The random variable $X ~ B (1250, 0.4)$

(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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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.