The Normal Distribution Calculator determines the probability density and Z-score for a given value based on the mean (μ) and standard deviation (σ). It applies the Gaussian distribution formula to find how likely a specific value occurs within a dataset. The probability density represents the height of the bell curve at that point, while the Z-score measures how far the value lies from the mean in terms of standard deviations. This tool is valuable for analyzing data patterns, performing hypothesis testing, and evaluating outcomes in statistics and quality control.