Invnorm Calculator
Calculate the inverse normal distribution (z-score) given a cumulative probability, mean, and standard deviation.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the InvNorm Calculator
- Enter Cumulative Probability (p): Input a value between 0 and 1 (e.g., 0.95 for the 95th percentile). This is the area under the normal curve to the left of the desired z-score.
- Set Mean (μ): Default is 0. Adjust if your distribution has a different mean.
- Set Standard Deviation (σ): Default is 1. Must be greater than 0. Use the same units as your data.
- Click "Calculate": The result shows the inverse normal value (x) = μ + z·σ, where z is the z-score corresponding to your probability.
Example: For p = 0.95, μ = 0, σ = 1, the result is approximately 1.644854 (the z-score for the 95th percentile).
Note: The calculator uses a rational approximation (Raffin, 2001) for accuracy. Inputs must be numeric; invalid entries trigger error messages.
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Frequently Asked Questions
InvNorm computes the inverse of the normal cumulative distribution function, returning the value at which the probability of a random variable with a given mean and standard deviation is less than or equal to a specified cumulative probability.
You need to provide the cumulative probability (between 0 and 1), the mean (μ), and the standard deviation (σ).
The inverse normal is undefined for probabilities exactly 0 or 1. The calculator will show an error if you enter values outside the open interval (0,1).
