Covers: Empirical Rule (68-95-99.7) · z-score calculation · normalcdf · inverse normal · comparing distributions. A z-table is included below.
±1σ → 68%
±2σ → 95%
±3σ → 99.7%
Symmetric → each half = ÷2
\(z = \dfrac{x - \mu}{\sigma}\)
x=value, μ=mean, σ=std dev
Tells how many σ from mean
Left tail: LB = −∞
Right tail: UB = +∞
Between: both bounds
P(X > x) = 1 − Φ(z)
Total area always = 1
Negative z → mirror!
Below mean → answer < 0.5
Higher z = better relative performance
Context always matters!
Each value = Φ(z) = P(Z ≤ z), the cumulative area from −∞ to z (left tail).