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Treating a normal density plot as a loss bound

The standardized plot’s −4 and +4 endpoints do not truncate the normal distribution.

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Read the displayed window

A finite plot samples density over a useful range. Inferring that losses outside its right endpoint have zero probability changes the distribution to a different bounded or truncated model.

Retain the original normal law

For positive dispersion, normal density remains positive at every finite standardized loss. Probability beyond +4 is small but positive. A selected quantile or tail mean describes a portion of that unbounded law, not the end of its support.

Keep the coordinate transformation

The calculator’s horizontal coordinate is z. A standardized coordinate +4 corresponds to μL+4σL loss units, not an unqualified four-currency-unit loss. The plot is shown in standardized coordinates to keep its density unit clear.

Name a different support assumption explicitly

If the task actually requires a cap, floor or truncated distribution, specify and calculate that model separately. Cropping a figure does not construct a valid truncated probability law.

Further references