Normal distribution calculator
Calculate probabilities for normal distributions: P(X ≤ x), z-scores, inverse normal, and bell curve areas.
xμσ
Normal distribution
The bell curve N(μ, σ²) with mean μ and standard deviation σ. 68-95-99.7 rule: 68% within 1σ, 95% within 2σ, 99.7% within 3σ.
Z-score
z = (x − μ)/σ converts to standard normal N(0,1). Then use z-tables or CDF.
Example
Test scores: μ=75, σ=10. Score of 85: z = (85−75)/10 = 1. P(X ≤ 85) = P(Z ≤ 1) ≈ 0.8413.
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