Statistics

Normal Distribution Calculator

This computes the same areas a z-table provides.

Find the z-score and probability for a normal value.

Calculated Output

Z-score 2

P(X < x) (%) 97.725

P(X > x) (%) 2.275

Formula: z = (x − μ) ÷ σ ; probability via normal CDF

Step-by-Step Breakdown

1. Values used:

2. Value (x) = 130

3. Mean (μ) = 100

4. Standard deviation (σ) = 15

6. Z-score = 2

7. P(X < x) = 97.725%

8. P(X > x) = 2.275%

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The math behind it

z = (x − μ) ÷ σ. The normal CDF gives P(X < x); the area above is 1 − that.

x 130, μ 100, σ 15 → z 2.0, P(X<130) ≈ 97.7%.

Z-table?

This computes the same areas a z-table provides.