In PERT, if a is the optimistic time, b is the pessimistic time, and m is the most likely time of an activity, what is the expected time (te)?

Introduction / Context:PERT (Program Evaluation and Review Technique) models activity duration uncertainty using three estimates: optimistic (a), most likely (m), and pessimistic (b). The expected time te is a weighted mean that emphasizes the most likely value while still incorporating extremes.

Given Data / Assumptions:

• Optimistic time = a
• Most likely time = m
• Pessimistic time = b
• Distribution is approximated by a Beta distribution on the activity's range [a, b].

Concept / Approach:PERT uses a weighting scheme that gives four times the weight to the most likely estimate, producing te = (a + 4m + b) / 6. This balances realism (m) with risk bounds (a and b).

Step-by-Step Solution:Identify the PERT expected time formula.Write it using standard keyboard symbols:te = (a + 4*m + b) / 6Compare against options to find the match.Select option with (a + 4m + b) / 6.

Verification / Alternative check:Variance is often computed as sigma^2 = ((b - a) / 6)^2, consistent with the same weighting logic used for te.

Why Other Options Are Wrong:

• (a + b + m) / 3: Simple average, ignores heavier weight for m.
• (2a + m + 3b) / 6 and (a + 2m + b) / 4 and (4a + m + b) / 6: Incorrect weightings; they misrepresent the Beta-based heuristic.

Common Pitfalls:Using an unweighted mean; swapping weights between a and b; forgetting the denominator 6 tied to 1 + 4 + 1 weighting.

Final Answer:te = (a + 4m + b) / 6