Normal distribution
X ~ N(μ, σ²). Bell curve. Use Z = (X − μ)/σ to standardise.
Y13 Stats. The normal is symmetric, defined by mean μ and variance σ². Z follows N(0, 1) (standard normal). Tables (Φ) or calculator function NormalCD.
Worked examples
X ~ N(50, 16); P(X < 56) = Φ((56−50)/4) = Φ(1.5) ≈ 0.9332.
68% within 1σ, 95% within 2σ, 99.7% within 3σ of the mean.
Inverse: find x such that P(X < x) = 0.95: z = 1.645, x = μ + 1.645σ.
Frequently asked questions
Why standardise?
Reduces every normal to N(0, 1), so one table or function suffices.
Continuity correction?
Used when approximating discrete with normal: P(X = k) ≈ P(k−0.5 < Y < k+0.5).