A Level Maths: The Normal Distribution Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Normal Distribution (OCR)
- Hypothesis Testing for the Sample Mean of a Normal Distribution (OCR)
- Hypothesis Testing for the Sample Mean of a Normal Distribution (Edexcel)
- Conditional Probability With The Normal Distribution (Edexcel)
- Normal Approximation to Binomial Distribution (Edexcel)
- Normal Approximation to Binomial Distribution (OCR Only) (OCR)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Discrete Distributions (inc. Binomial Distribution) — binomial is the natural comparison
- Averages and Spread — mean and standard deviation underpin the distribution
- Binomial Hypothesis Testing — provides the hypothesis testing framework
A Level Maths the normal distribution is the workhorse continuous distribution of Year 2 statistics. Many real-world quantities — heights, weights, exam marks, measurement errors — are approximately normally distributed, making this the most-used distribution in applied statistics. You learn to work with it, use it for probabilities, and test hypotheses about the mean.
The normal distribution $X \sim N(\mu, \sigma^2)$ has mean $\mu$ and variance $\sigma^2$ (so standard deviation $\sigma$). Its bell-shaped curve is symmetric about $\mu$. You use your calculator to find probabilities directly (the formula for the probability density function is not required). You also use the standard normal distribution $Z \sim N(0, 1)$, with $Z = \frac{X – \mu}{\sigma}$ (standardising), for working with normal tables when needed. The empirical rule — that approximately $68\%$ of values lie within one standard deviation of the mean, $95\%$ within two, and $99.7\%$ within three — gives quick sanity checks. You also apply a normal approximation to the binomial distribution $B(n, p)$ as $N(np, np(1-p))$ when $n$ is large and $p$ is moderate, and run hypothesis tests on the mean of a normally distributed population.
The normal distribution is part of the Statistics strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: the distribution is specified by VARIANCE $\sigma^2$ in $N(\mu, \sigma^2)$, but your calculator usually wants STANDARD DEVIATION $\sigma$ — make sure you use the right input; $P(X = k) = 0$ for ANY specific value of a continuous random variable, so $P(X \le k)$ and $P(X < k)$ are equal (unlike for discrete variables); for the normal approximation to the binomial, a continuity correction (shifting by $\pm 0.5$) is often required; and the standard error of the sample mean is $\sigma/\sqrt{n}$, not just $\sigma$.