Normal Distribution & Standardization

Set the mean μ and standard deviation σ, then slide a boundary to shade the area under the curve. The shaded area IS the probability, and every boundary is a z-score in disguise: z = (x − μ) / σ.

Try: set μ = 0, σ = 1, mode Between, bounds −1 and +1 → area ≈ 0.6827 (the 68% empirical rule). Move bounds to −1.96 and +1.96 → ≈ 0.95. Then mode Right tail, μ = 100, σ = 15, cutoff 130 → P(X > 130) ≈ 0.0228 (IQ above 130).