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Separate a point from an interval
For a continuous normal loss law with positive dispersion, probability at a single specified loss is zero. The density at that point can still be positive. Probabilities arise by integrating the density across an interval.
Read the standard normal scale
The standard normal density at z=0 is about 0.398942 per z unit. That number does not mean a 39.8942% probability of exactly zero. The area over the whole real line is one.
Retain the density unit
| Quantity | Unit or meaning |
|---|---|
| Loss x | Original loss units |
| Loss density fL(x) | Probability per loss unit |
| Standardized z | Dimensionless standardized loss |
| Standard density φ(z) | Probability per z unit |
| Interval area | Dimensionless probability |
Read the calculator’s plotted curve
The tool plots standard normal density against z. It does not show a discrete probability bar at each sampled point. Sampling more curve coordinates would improve a visual approximation, not create additional probability mass.