Use this tool to calculate the value at a given percentile of a standard normal distribution, which is essential for statistical analysis and probability estimation.

## Inverse Normal Distribution Calculator

### How To Use This Calculator

Enter the probability, mean, and standard deviation for the inverse normal distribution you’re trying to calculate, and click “Calculate”. The result displayed is the value at which the cumulative distribution function (CDF) of a normal distribution equals the input probability.

### How It Calculates the Results

This calculator uses a precomputed table of z-scores (standard normal distribution) to find the z-score that corresponds to the given probability. It then uses the entered mean (μ) and standard deviation (σ) to adjust the standard normal distribution to your specific normal distribution, using the formula: [X = μ + Z * σ]

### Limitations of the Calculator

The accuracy of the calculator is limited by the z-table provided. A full table includes z-scores for every three decimal places, but for the sake of simplicity, only a few are listed. For precise calculations, a complete z-table should be implemented. Additionally, this calculator assumes the input probability, mean, and standard deviation are accurate and that the distribution in question is truly normal.