One number can make an uncertain activity look more certain than it is. Three-point estimating keeps the range visible, while PERT turns that range into a weighted expected duration.
Three estimates tell one story
An estimator supplies three realistic durations for the same activity:
- Optimistic (O): the duration under favorable conditions that are still realistically possible.
- Most likely (M): the duration expected to occur most often.
- Pessimistic (P): the duration under unfavorable conditions that are still realistically possible.
The values should describe plausible conditions, not fantasy best cases or disaster scenarios in which the work never finishes.
The PERT weighted estimate
Traditional PERT uses this weighted calculation:
Expected duration = (O + 4 × M + P) ÷ 6
The most likely estimate receives four of the six weights. The optimistic and pessimistic estimates receive one weight each. For the museum activity:
(6 + 4 × 10 + 20) ÷ 6 = 66 ÷ 6 = 11 days
An ordinary average would produce 12 days: (6 + 10 + 20) ÷ 3. That is a useful distractor because it uses every number, but it ignores the stated PERT weighting.
Expected does not mean guaranteed
The 11-day result is an estimate for schedule analysis. It is not automatically a deadline, commitment, contingency reserve, or promise that the fossil mount will finish on that exact day. The model is only as useful as its inputs and the schedule logic around the activity.
Reading the spread
Traditional PERT also approximates the activity's standard deviation as:
Standard deviation = (P − O) ÷ 6
For the museum activity, (20 − 6) ÷ 6 is about 2.3 days. Variance is the standard deviation squared, or about 5.4 days². A wider optimistic-to-pessimistic range produces a larger spread and signals more uncertainty.
The live lab shows an approximate one-standard-deviation band for orientation. It should not be treated as a guaranteed completion window.
A quick routine for the exam
- Identify the optimistic, most likely, and pessimistic values.
- Confirm that O ≤ M ≤ P.
- Multiply the most likely value by four.
- Add all six weights and divide by six.
- Check what the question actually asks for: expected duration, standard deviation, variance, or a different estimating method.
The weighted formula and standard-deviation approximation are consistent with PMI references on PERT and three-point estimating.