What is the Normal Distribution Calculator?

The Normal Distribution Calculator is a statistical tool designed to help students, researchers, and analysts quickly determine probabilities and z-scores for normally distributed data. By entering the mean, standard deviation, and a specific value of X, the calculator computes the corresponding z-score and the cumulative probability P(X≤x)P(X \le x)P(X≤x). This allows users to understand the relative position of a data point within a distribution and assess probabilities without complex manual calculations, ensuring precise insights for academics, business analytics, or scientific research.

How to Use:

1. Enter Mean (μ): Input the average or expected value of your dataset.
2. Enter Standard Deviation (σ): Input the spread or variability of your data. Ensure it is greater than zero.
3. Enter Value of X: Input the specific value you want to analyze within the distribution.
4. Click “Calculate”: The tool computes the z-score and cumulative probability.
5. Review Result: The output shows the mean, standard deviation, value of X, z-score, and the probability P(X≤x)P(X \le x)P(X≤x) in a clear, easy-to-read format, along with a visual emphasis for quick interpretation.