Statistical Distributions — A-Level Mathematics Revision
Revise Statistical Distributions 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 Normal DistributionWhat is Statistical Distributions?
Statistical distributions at A-Level introduce the concept of a random variable and its probability distribution. You will learn about the binomial distribution and its properties, and be able to calculate probabilities for a given number of successes in a fixed number of trials.
Board notes: All A-Level Maths boards (AQA, Edexcel, OCR) cover the binomial distribution. The use of cumulative distribution tables and the complexity of the problems can vary slightly.
Step-by-step explanationWorked example
A fair coin is tossed 10 times. What is the probability of getting exactly 6 heads? This is a binomial distribution with n=10, p=0.5, and r=6. P(X=6) = 10C6 * (0.5)^6 * (0.5)^4 = 210 * (0.5)^10 = 210/1024 = 105/512.
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Common mistakes
- 1Confusing the conditions for a binomial distribution. The four conditions are: a fixed number of trials, each trial has two possible outcomes (success or failure), the trials are independent, and the probability of success is constant for each trial.
- 2Incorrectly using the formula for binomial probability, P(X=r) = nCr * p^r * (1-p)^(n-r).
- 3Making errors when using cumulative distribution tables for the binomial distribution. It's important to understand whether the tables give P(X<=r) or P(X>=r).
Statistical Distributions exam questions
Exam-style questions for Statistical Distributions with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Statistical Distributions
Core concept
Statistical distributions at A-Level introduce the concept of a random variable and its probability distribution. You will learn about the binomial distribution and its properties, and be able to calc…
Frequently asked questions
What is a discrete random variable?
A discrete random variable is a variable that can only take on a finite or countable number of values. For example, the number of heads when a coin is tossed 10 times is a discrete random variable.
What is the expected value of a binomial distribution?
The expected value (or mean) of a binomial distribution is given by the formula E(X) = np, where n is the number of trials and p is the probability of success.