Normal Distribution Calculator

Normal Distribution Formula

Worked Example

X normal with μ = 50 and σ = 10, between 40 and 65:

1. z = (x − μ)/σ: z_a = -1, z_b = 1.5
2. P = Φ(1.5) − Φ(-1) = 0.77453754

z for b: 1.5 · As a percentage: 77.453754 %

GATE tip

GATE gives Φ values in the question when needed. Convert to z first, use symmetry Φ(−z) = 1 − Φ(z), and check the answer against the 68-95-99.7 rule.

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• De Moivre’s Theorem Calculator

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Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.