Normal Distribution — A-Level Mathematics Revision
Revise Normal Distribution for A-Level Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Statistical Hypothesis TestingWhat is Normal Distribution?
The normal distribution is a continuous probability distribution that is symmetrical about the mean. It is a fundamental concept in statistics, used to model many real-world phenomena. You will learn to use the standard normal distribution and its tables to find probabilities.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover the normal distribution. The use of the normal distribution to approximate the binomial distribution is a key topic for all boards.
Step-by-step explanationWorked example
The heights of a certain population of men are normally distributed with a mean of 175cm and a standard deviation of 5cm. What is the probability that a randomly selected man is taller than 180cm? First, standardize the value: Z = (180 - 175) / 5 = 1. Now, we want to find P(Z > 1). From the standard normal distribution tables, P(Z < 1) = 0.8413. So, P(Z > 1) = 1 - 0.8413 = 0.1587.
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Common mistakes
- 1Forgetting to standardize the variable before using the standard normal distribution tables. You must convert your variable X to the standard normal variable Z using the formula Z = (X - μ) / σ.
- 2Making errors when using the standard normal distribution tables, particularly with negative values of Z and when finding probabilities for ranges of values.
- 3Confusing the normal distribution with the binomial distribution. The normal distribution is continuous, while the binomial distribution is discrete.
Normal Distribution exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Normal Distribution
Core concept
The normal distribution is a continuous probability distribution that is symmetrical about the mean. It is a fundamental concept in statistics, used to model many real-world phenomena. You will learn …
Frequently asked questions
What are the properties of the normal distribution?
The normal distribution is bell-shaped and symmetrical about the mean. The mean, median, and mode are all equal. About 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
When can you use the normal distribution to approximate the binomial distribution?
You can use the normal distribution to approximate the binomial distribution when n is large and p is close to 0.5. A common rule of thumb is that the approximation is good if np > 5 and n(1-p) > 5.