Confidence and a matter of range

It's all a matter of confidence: confidence in statistical terms is the cumulative probability over a range of values.  It's a little more handy for project managers because it only expresses an approximation and a judgement, and both of these ideas allow for some leeway.

Using a bell-shaped Normal (probability density) distribution as an example--and, because of the Central Limit Theorem, this is a reasonable example to look at-- risk managers calculate cumulative by summing the height x width area under the curve.  In the figure, we see the so-called "S" curve superimposed on the distribution.  The "S" curve is the cumulative probability.

Confidence is an expression of cumulative probability over a range.  In the example shown, the confidence is "outcome will be equal to, or less than, 4 in 81% of the trials".  Obviously, the 81% is calculated by subtracting 19% from 100%.  The "precision" here is just an artifact of the tool.  The judgement is about the "80 - 20" rule, and the figure is an illustration.

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