STA009 · Probability & statistics · Classes 11–12
Gaussian (Normal) Curve
The bell-shaped normal distribution curve.
Gaussian (Normal) Curve📐 Formula
y = [1/(σ√(2π))] e^(−(x − μ)²/(2σ²)); about 68% of values lie within μ ± σ, 95% within μ ± 2σ
✏️ Worked example
μ = 0, σ = 1: peak height ≈ 0.399; 68% between −1 and 1.
🌍 Where it is used
Exam scores, heights and measurement errors.
❓ Quick check
About what % of data lies within one SD of the mean?