Binomial and Normal Distributions
Selecting, calculating with and interpreting binomial and normal models, standardisation, parameters and normal approximations with continuity correction.
How to study A-level Mathematics
Define the objects and conditions, select a representation, execute a justified method, then validate and interpret the result.
Core concepts
Concept 1
A binomial model counts successes across a fixed number of independent trials with constant success probability.
Exam cue: Justify the distribution assumptions before calculating.
Concept 2
A normal distribution is continuous and determined by its mean and variance, with probabilities represented by areas.
Exam cue: Translate verbal inequalities carefully and use complements when efficient.
Concept 3
A normal approximation to a binomial requires suitable parameters and a continuity correction when moving from discrete counts to continuous boundaries.
Exam cue: Apply the half-unit continuity correction to the discrete boundary before standardising.
Risk pitfalls and guardrails
Using a binomial model when trial probabilities change or trials are dependent.
Guardrail: Do not replace proof with examples, model conditions with unstated assumptions, or mathematical interpretation with unverified calculator output.
Confusing variance with standard deviation.
Guardrail: Do not replace proof with examples, model conditions with unstated assumptions, or mathematical interpretation with unverified calculator output.
Omitting or reversing a continuity correction.
Guardrail: Do not replace proof with examples, model conditions with unstated assumptions, or mathematical interpretation with unverified calculator output.
Memory anchors
Binomial Model
A binomial variable counts successes in fixed independent Bernoulli trials with constant p.
Binomial Mean
For X~B(n,p), the mean is np.
Binomial Variance
For X~B(n,p), the variance is np(1-p).
Normal Distribution
A normal distribution is a continuous symmetric model determined by μ and σ².
Continuity Correction
A continuity correction shifts a discrete count boundary by one half for a continuous approximation.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Which conditions support a binomial model?
If X~B(10,0.3), find P(X=0).
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”