Use it to set cut-offs, for example the score needed to be in the top 10%.
How to use the Inverse Normal Distribution Calculator
- Mean (μ)
- Standard deviation (σ)
- Area to the left
Results update as you type, and every field accepts the units shown in its menu.
How it works
Find the z-score for the probability with the inverse normal function, then convert to the original scale.
Inputs explained
| Field | What to enter |
|---|---|
| Mean (μ) | A number |
| Standard deviation (σ) | A number |
| Area to the left | In % |
What each result means
- z-score = ninv([Area to the left]÷100)
- Value x = [Mean (μ)] + [Standard deviation (σ)]×[z-score]
Example values
How the main result changes when Mean changes and everything else stays at the example values above:
| Mean (μ) | Value x |
|---|---|
| 50 | 69.2233 |
| 75 | 94.2233 |
| 100 | 119.2233 |
| 125 | 144.2233 |
| 150 | 169.2233 |
| 200 | 219.2233 |
Formula
x = μ + σ × Φ⁻¹(p)Worked example
Inputs — Mean (μ): 100; Standard deviation (σ): 15; Area to the left: 90 %.
Results — z-score = 1.2816; Value x = 119.2233.
Frequently asked questions
What is z for the 95th percentile?
About 1.645.
How do I get a two-sided cut-off?
Use (1 + confidence)/2, e.g. 97.5% for a 95% interval.
What formula does the Inverse Normal Distribution Calculator use?
x = μ + σ × Φ⁻¹(p).