Normal Distribution Calculator

Calculate probabilities and Z-scores for any normal distribution with visual bell curve representation.

Distribution Parameters

Set μ, σ, and select probability mode

Probability Mode

Mean (μ)

Standard Deviation (σ)

X₂ (upper bound)

Probability Density Probability

Z-Score

Enter distribution parameters above and tap Calculate.

Step-by-step Solution

Normal Curve Visualization

Z-Table Reference

Z = 1.00

0.8413

Z = 1.645

0.9500 (90%)

Z = 1.96

0.9750 (95%)

Z = 2.576

0.9950 (99%)

Z-Score Formula

Z = (X - μ) / σ

X = Observed value
μ = Population mean
σ = Population standard deviation

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