Inverse Normal Calculator (InvNorm)
Find the x-value or z-score for a given probability in a normal distribution. Commonly used for finding critical values in hypothesis testing.
Calculator Input
Enter value between 0 and 1
Use 0 for standard normal
Use 1 for standard normal
Common Critical Z-Values
| Confidence Level | α (Alpha) | α/2 | z (Two-Tail) |
|---|---|---|---|
| 50% | 0.500 | 0.2500 | ±0.000 |
| 80% | 0.200 | 0.1000 | ±1.282 |
| 90% | 0.100 | 0.0500 | ±1.645 |
| 95% | 0.050 | 0.0250 | ±1.960 |
| 99% | 0.010 | 0.0050 | ±2.576 |
| 99.9% | 0.001 | 0.0005 | ±3.291 |
Understanding Inverse Normal Distribution
What is InvNorm?
The inverse normal function (also called the quantile function or percent-point function) finds the value x such that P(X ≤ x) = p for a given probability p. It's the reverse of the cumulative distribution function (CDF).
The Formula
Where z is the z-score corresponding to the probability, μ is the mean, and σ is the standard deviation.
Common Applications
- Finding critical values for confidence intervals
- Determining rejection regions in hypothesis testing
- Quality control limits (e.g., Six Sigma)
- Risk analysis (Value at Risk calculations)
- Setting percentile-based thresholds
TI-84 Calculator Equivalent
On a TI-84 calculator, this is the invNorm function found under:
Related Statistics Tools
Note: This calculator uses numerical approximations that are accurate to several decimal places. For critical applications or research, verify results with statistical software or tables.
About Inverse Normal Calculator - InvNorm Critical Values
Find x-values and z-scores for given probabilities in normal distributions. Essential for finding critical values in hypothesis testing.
Our **Inverse Normal Calculator** (InvNorm) finds the value x such that P(X ≤ x) = p. Enter a probability to get the corresponding z-score or x-value. For probability calculations, see our Normal CDF Calculator.
The inverse normal function is crucial for finding critical values in hypothesis testing, constructing confidence intervals, and determining percentiles. This is the inverse of the CDF function.
Supports left-tail, right-tail, and center probability modes. The calculator provides both z-scores (for standard normal) and x-values (for general normal distributions).
Key Features
Why Use This Tool?
Common Use Cases
Statistics: Finding critical values for tests.
Research: Constructing confidence intervals.
Quality Control: Setting specification limits.
Finance: Value at Risk (VaR) calculations.
Related Tools
How to Use
Enter the probability (area)
Select tail type
Set mean and standard deviation
Click Calculate
View z-score and x-value