The Binomial Distribution and Sampling Distribution of the Mean
Bernoulli trials, the binomial distribution B(n,p), expected value and variance, the sampling distribution of the sample mean x̄, and the Central Limit Theorem — covering ME1-12-06 in full.
Active lessons
7
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 6 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
7 of 7 active
Lesson 1
Bernoulli Trials
Practise bernoulli trials with concise examples and mastery checks.
Lesson 2
Binomial Probabilities
Practise binomial probabilities with concise examples and mastery checks.
Lesson 3
Mean and Variance
Practise mean and variance with concise examples and mastery checks.
Lesson 4
Binomial Exam Practice
Practise binomial exam practice with concise examples and mastery checks.
Lesson 5
Distribution of the Sample Mean
Define population and sample, derive E(x̄) = μ and Var(x̄) = σ²/n, and examine the effect of sample size on the spread of x̄.
Lesson 6
The Central Limit Theorem
State the CLT, convert x̄ to z-scores, and calculate probabilities about sample means using normal distribution values.
Lesson 7
Prior Knowledge Revision: Probability and Combinations
Activate prior knowledge for the Binomial Distribution: probability rules (complement, addition, multiplication), combinations C(n,r), and expected value of a discrete random variable.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.