What is the Normal Distribution Calculator?

The Normal Distribution Calculator estimates the probability of a value occurring within a normal (Gaussian) distribution based on the mean (μ) and standard deviation (σ). It calculates the Z-score for a given value and approximates the cumulative probability P(X ≤ x). This helps users analyze data, understand how likely a value is relative to the distribution, and make data-driven decisions in statistics, quality control, or research.

How to Use:

1. Enter Value (X): Type the specific data point you want to evaluate (e.g., 85).
2. Enter Mean (μ): Input the average value of the dataset (e.g., 80).
3. Enter Standard Deviation (σ): Input the standard deviation to measure spread (σ ≠ 0, e.g., 5).
4. Click “Calculate”: The calculator will compute the Z-score and the probability P(X ≤ X).
5. Review the Result: Use the Z-score and probability to understand how your value compares to the overall distribution and make statistical insights.