Normal Distribution Calculator — PDF, CDF, and Inverse CDF

What this calculator is

The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.

Key features

• Immediate results as you change inputs
• Transparent assumptions and explainable outputs
• Works well with the built‑in Notebook for saving scenarios

Formula

PDF: f(x) = (1/(σ√(2π))) · exp( −(1/2)·((x−μ)/σ)^2 )
CDF: Φ(x) = P(X ≤ x)
Quantile: x = Φ^{-1}(p)

Quick examples

• normalpdf(0, 0, 1) # ≈ 0.398942
• normalcdf(1.96, 0, 1) # ≈ 0.975002
• normalinv(0.975, 0, 1) # ≈ 1.96
• # Symmetry check for standard normal normalcdf(-1.96, 0, 1) - (1 - normalcdf(1.96, 0, 1))

Verification tips

• PDF values are densities, not probabilities. Probabilities come from areas (CDF differences).
• For standard normal, Φ(0)=0.5 and Φ(±1.96)≈0.975/0.025.
• σ must be positive; if σ=0 the distribution is undefined.

Common mistakes

• Confusing PDF with CDF (density vs probability).
• Using σ as variance instead of standard deviation.
• Forgetting that normalcdf returns P(X ≤ x).

How to use it (quick steps)

1. Decide whether you need PDF, CDF, or an inverse CDF (quantile).
2. Open the Statistics Calculator.
3. Use normalpdf(x, μ, σ) for density, normalcdf(x, μ, σ) for probability, and normalinv(p, μ, σ) for quantiles.
4. Sanity check with symmetry (for μ=0, σ=1) and known values (e.g., Φ(0)=0.5).
5. Document μ, σ, and your interpretation (probability vs density).

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FAQ

Tip: For reproducible work, save your inputs and reasoning in Notebook.