In a hospital renovation project using PERT data, what is the expected completion time for activity A given optimistic 7, most likely 9, pessimistic 14 days?

• A. 7.5 days
• B. 9.5 days
• C. 10.0 days
• D. 12.0 days

Answer: (B)

The PERT approach uses a weighted average where the most likely duration has the greatest influence: E = (O + 4M + P) / 6. With optimistic 7 days, most likely 9 days, and pessimistic 14 days, you get E = (7 + 4×9 + 14) / 6 = (7 + 36 + 14) / 6 = 57 / 6 = 9.5 days. So the expected completion time is 9.5 days. This weighting pulls the estimate toward the most probable duration, reflecting the belief that 9 days is the best realistic duration while still accounting for uncertainty from the optimistic and pessimistic bounds. For comparison, a simple average of the three values would give 10 days, which demonstrates why PERT uses the 4M weight to produce a slightly lower/weighted estimate.