PERT Analysis MCQ with answer and solution

Concept

Expected activity duration in PERT

Formula

t_e = (t_o + 4·t_m + t_p) / 6

Step-by-step solution

1. Given estimates: - Optimistic time (t_o) = 7 days - Most likely time (t_m) = 15 days - Pessimistic time (t_p) = 17 days 2. Apply the PERT expected time formula: t_e = (t_o + 4·t_m + t_p) / 6 3. Compute numerator: 7 + 4(15) + 17 = 7 + 60 + 17 = 84. 4. Divide by 6: t_e = 84 / 6 = 14 days. 5. Therefore, option B (14 days) is correct. Answer: B

Explanation

In PERT analysis, the expected activity duration (t_e) follows a beta distribution and is calculated as t_e = (t_o + 4·t_m + t_p) / 6. Substituting t_o = 7 days, t_m = 15 days, and t_p = 17 days gives t_e = (7 + 4×15 + 17) / 6 = 84 / 6 = 14 days.

Why the other options are wrong

A) 12 is less than the expected value. C) 16 days overestimates the duration by over-weighting the pessimistic estimate. D) 18 days exceeds even the pessimistic duration.

Shortcut

t_e = (7 + 4×15 + 17) / 6 = 84 / 6 = 14.

Common mistake

Taking a simple arithmetic mean (7 + 15 + 17)/3 = 13 days instead of weighting the most likely time by 4 in the beta distribution.