Statistics

Inverse Normal Distribution Calculator

Find the value with a given cumulative probability (inverse CDF).

Calculated Output

Value x 1.96

Z-score 1.96

Formula: x = mean + z·sd, z = Φ⁻¹(p)

Step-by-Step Breakdown

1. Values used:

2. Cumulative probability = 0.975

3. Mean = 0

4. Standard deviation = 1

6. Value x = 1.96

7. Z-score = 1.96

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The math behind it

It inverts the normal CDF: x = mean + z·sd, where z = Φ⁻¹(p). Computed with Acklam's algorithm.

p 0.975, standard normal → z ≈ 1.96.

What is z for 95% two-tailed?

About ±1.96, the cutoffs at p = 0.025 and 0.975.