What the project manager does not know is the standard deviation or the variance of the Normal distribution. It is quite proper to ask of what real utility it is to know that the output milestone is Normal with an expected value (mean value) but have no other knowledge of the distribution. The answer is straightforward: either a schedule simulation can be run to determine the distribution parameters or, if there is no opportunity to individually estimate the tasks on the WBS, then the risk estimation effort can be moved to the output milestone as a practical matter.

At this point, there really is not an option about selecting the distribution since it is known to be Normal; if expected values have been used to compute the critical path, or some reasonable semblance of expected values has been used, then the mean of the output milestone is calculable. It then remains to make some risk assessment of the probable underrun. Usually we calculate the underrun distance from the mean as a most optimistic duration. Once done, this underrun estimate is identically the same as the distance from the expected value to the most pessimistic estimate. Such a conclusion is true because of the symmetry of the Normal distribution; underrun and overrun must be symmetrically located around the mean.

The last estimate to make is the estimate for the standard deviation. The standard deviation estimate is roughly one-sixth of the distance from the most optimistic duration estimate to the most pessimistic estimate.

Next, the Normal distribution for the outcome milestone is normalized to the standard Normal distribution. The standard Normal curve has mean = 0 and σ = 1. Once normalized, the project manager can apply the Normal distribution confidence curves to develop confidence intervals for communicating to the project sponsor