PERT time estimates: In PERT, optimistic, pessimistic, most likely, and expected time estimates refer to what?

Introduction / Context:
PERT quantifies schedule uncertainty by describing each activity with three time estimates and combining them into an expected value. This approach is useful when historical data are limited or the work is novel.

Given Data / Assumptions:

• For each activity: optimistic (a), most likely (m), pessimistic (b) durations are assessed.
• Expected time te is computed using a weighted average.
• Variance helps assess schedule risk along paths.

Concept / Approach:
PERT uses the relation te = (a + 4m + b) / 6 and variance sigma^2 = ((b - a) / 6)^2 for each activity, assuming a beta-like distribution. These estimates belong to activities, not events.

Step-by-Step Solution:
Define optimistic time (a): minimum plausible duration if everything goes well.Define pessimistic time (b): maximum plausible duration under adverse conditions.Define most likely time (m): modal estimate under normal conditions.Compute expected time (te) for scheduling and risk analysis.

Verification / Alternative check:
Summing expected times along the critical path yields the expected project duration; combining variances gives an estimate of completion probability.

Why Other Options Are Wrong:
Each individual option is correct; therefore the only comprehensive choice is 'All the above.'

Common Pitfalls:
Applying PERT formulas to events; confusing deterministic CPM durations with PERT probabilistic estimates; ignoring variance when communicating schedule risk.

Final Answer:
All the above.