Question

In PERT technique, the time estimate of activities and probability of their occurrence follows:

• A. Gumbel distribution
• B. Beta distribution
• C. Poisson distribution
• D. Normal distribution

Hint:

Expected time ($t_e$) for the Beta distribution is calculated as: $t_e = \frac{t_o + 4t_m + t_p}{6}$. Note how the "Most Likely" time is weighted four times more than the extremes!

Answer 1

The Correct Option is B

Concept: The Program Evaluation and Review Technique (PERT) is a probabilistic method used when activity durations are uncertain. It uses three time estimates: Optimistic ($t_o$), Most Likely ($t_m$), and Pessimistic ($t_p$).

Step 1: Activity Distribution vs. Project Distribution.
It is important to distinguish between the individual activity and the overall project:
• Individual Activity: The time for a single activity in PERT is assumed to follow a $\beta$-distribution (Beta distribution). This is because the distribution is flexible and can be skewed to account for the fact that delays are more likely than finishing early.
• Total Project Duration: According to the Central Limit Theorem, the total time for the critical path (sum of many activities) follows a Normal distribution.

Step 2: Conclusion.
Since the question asks about the time estimate of "activities," the answer is the Beta distribution.