Question

In PERT analysis, the time estimates of activities and probability of their occurrence follow

• A. Normal distribution
• B. Gamma distribution
• C. Beta distribution
• D. Poisson's distribution

Hint:

In PERT, individual activity durations are modeled using a Beta distribution due to its flexibility in representing skewed distributions and its bounded nature between optimistic and pessimistic time estimates. The overall project duration, however, is often approximated by a Normal distribution due to the Central Limit Theorem.

Answer 1

The Correct Option is C

Step 1: Understand time estimation in PERT.
PERT is a probabilistic project management technique, meaning it accounts for uncertainty in activity durations. Instead of a single time estimate, PERT uses three time estimates for each activity: optimistic time ($t_o$), most likely time ($t_m$), and pessimistic time ($t_p$).
Step 2: Identify the probability distribution for activity times.
In PERT, the duration of an individual activity is assumed to follow a Beta distribution. The Beta distribution is chosen because it can model a range of different shapes, is bounded by the optimistic and pessimistic time estimates, and allows for the most likely time to be skewed.
Step 3: Identify the probability distribution for project completion time.
While individual activity times follow a Beta distribution, the total project completion time (which is the sum of many activity times) is generally assumed to follow a Normal distribution based on the Central Limit Theorem. This is important for calculating the probability of project completion by a certain date.
Step 4: Evaluate the given options based on activity time estimates.
The question specifically asks about "time estimates of activities and probability of their occurrence."
Option 1: Normal distribution. This applies to the overall project completion time, not individual activity times directly in the initial estimation phase for each activity.
Option 2: Gamma distribution. Not typically used for activity time estimates in standard PERT.
Option 3: Beta distribution. This is the correct distribution assumed for individual activity durations in PERT analysis.
Option 4: Poisson's distribution. This is used for events occurring over a fixed interval of time or space (e.g., number of arrivals per hour), not for activity durations.
The final answer is $\boxed{\text{3}}$.