Dax Function: NORM.S.INV
Reviewed by Neetu Singla — Founder, Lets Viz Technologies — AI & Data Consultant. Last reviewed April 9, 2026.Category: Statistical Functions
The NORM.S.INV function in Power BI is a DAX function used to calculate the inverse of the standard normal cumulative distribution function (CDF). Given a probability, it returns the corresponding z-score for a standard normal distribution (mean = 0, standard deviation = 1).
Purpose of the Function
Determine the z-score corresponding to a given cumulative probability.
Type of Calculations
Computes the inverse cumulative distribution.
Practical Use Cases
- Finding critical z-scores in hypothesis testing.
- Calculating cutoff values in control charts.
- Estimating thresholds for risk assessment.
NORM.S.INV(<probability>)</probability>
| Parameter | Type | Description |
|---|---|---|
<Probability> | Scalar | A numeric value representing the cumulative probability. Must be between 0 and 1 (exclusive). |
How Does NORM.S.INV Dax Works
Mathematical Principle
The function inverts the cumulative distribution function (CDF) of the standard normal distribution:
Input: A probability p, where 0 < p < 1.
Output: A z-score that satisfies:
F(z)=p
Where F(z) is the cumulative distribution function of the standard normal distribution.
For example:
If p = 0.5, z = 0 (the median of the standard normal distribution).
If p = 0.025, z = −1.96 (common in 95% confidence intervals).
What Does It Return?
The NORM.S.INV function returns:
A numeric value representing the z-score corresponding to the cumulative probability.
The returned z-score can range from −∞ to , depending on the input probability.
When Should We Use It?
Critical Values: Identify zz-scores for statistical tests (e.g., significance levels in t-tests or z-tests).
Threshold Analysis: Calculate cutoff values for specific probabilities.
Quantile Calculations: Find percentiles in standardized datasets.
Examples
Basic Usage :
Find the z-score for a cumulative probability of 0.975:
NORM.S.INV(0.975)
Output: Approximately 1.96.
Column Usage
Compute z-scores for a column of cumulative probabilities:
ADDCOLUMNS(
Probabilities,
"ZScore",
NORM.S.INV(Probabilities[Probability])
)
Use Case: Add a column of z-scores corresponding to the cumulative probabilities.
Advanced Usage
Combine with other DAX functions to compute critical zz-scores for varying confidence levels:
NORM.S.INV(1 - (1 - ConfidenceLevel) / 2)
Use Case: Calculate two-tailed critical values for different confidence levels dynamically.
Tips and Tricks
Valid Input Range: Ensure probabilities are strictly between 0 and 1; values outside this range will result in errors.
Standard Normal Assumption: The function assumes a mean of 0 and standard deviation of 1. Use
NORM.INVfor non-standard distributions.Error Handling: Wrap the function in an error-checking mechanism for dynamic datasets to handle out-of-range probabilities.
Performance Impact of NORM.S.INV DAX Function:
Efficient for individual calculations.
For large datasets, consider precomputing critical values for common probabilities.
Related Functions You Might Need
NORM.DIST: Calculates cumulative probability or density for a normal distribution with a given mean and standard deviation.
NORM.INV: Finds the value for a given probability in a normal distribution with a specified mean and standard deviation.
NORM.S.DIST: Computes the cumulative or density function for the standard normal distribution.
Want to Learn More?
For more information, check out the official Microsoft documentation for NORM.S.INV You can also experiment with this function in your Power BI reports to explore its capabilities.
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It calculates the -score corresponding to a given cumulative probability in the standard normal distribution.
Probabilities must be between 0 and 1 (exclusive).
NORM.S.INV calculates the inverse cumulative probability (-score), while NORM.S.DIST calculates the cumulative probability or density for a given z-score.
No, it is designed specifically for the standard normal distribution. Use NORM.INV for custom distributions.
Use error-handling techniques like IF statements or validation checks to ensure probabilities are within the valid range.
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