Statistical distributions (A2 Unit 4: Applied Mathematics B) — WJEC A-Level Mathematics
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Statistical distributions (A2 Unit 4: Applied Mathematics B) explained
For a Normal variable X ~ N(μ, σ²), probabilities correspond to areas under the bell curve, evaluated via calculator functions (Normal CD) or standardisation.
Read the full explanation
Standardisation maps X to the standard Normal variable Z ~ N(0, 1) via Z = (X − μ)/σ. Candidates calculate P(X < b), P(X > a) = 1 − P(X < a), and P(a < X < b) = P(X < b) − P(X < a). In inverse Normal problems, given a cumulative probability p, candidates find the corresponding critical value x using calculator Inverse Normal functions, or by finding z from tables and solving x = μ + zσ. Setting up simultaneous equations enables solving for unknown μ and σ.
Your focus
- Calculate probabilities for Normal distributions using statistical calculator functions and standardisation.
- Determine values corresponding to given percentiles using inverse Normal calculator operations.
- Formulate and solve simultaneous equations to find unknown mean μ and standard deviation σ.
Statistical distributions (A2 Unit 4: Applied Mathematics B) exam tips
Marking Points
- applying the standardisation formula Z = (X − μ) / σ correctly
- evaluating Normal probabilities P(a < X < b) using calculator statistical functions
- using Inverse Normal functions to find values corresponding to given cumulative probabilities
- setting up and solving simultaneous equations to determine unknown parameters μ and σ
Examiner Tips
- 💡Always check whether the given parameter is variance σ² or standard deviation σ before calculating.
- 💡Sketch a bell curve, shade the required region, and mark μ to check that your answer is reasonable.
Common Mistakes
- using the variance σ² instead of standard deviation σ in the standardisation formula Z = (X − μ)/σ
- confusing upper-tail probabilities with lower-tail areas when using Inverse Normal calculator functions