Question Two:

A project manager is tasked with estimating the duration of three critical tasks in a construction project: foundation laying, building structure, and interior finishing. The manager gathers input from relevant stakeholders and obtains the following estimates for each task:

Foundation Laying:

Optimistic Time $($O$)$: $5$ days

Most Likely Time $($M$)$: $8$ days

Pessimistic Time $($P$)$: $12$ days

Building Structure:

Optimistic Time $($O$)$: $10$ days

Most Likely Time $($M$)$: $15$ days

Pessimistic Time $($P$)$: $20$ days

Interior Finishing:

Optimistic Time $($O$)$: $7$ days

Most Likely Time $($M$)$: $10$ days

Pessimistic Time $($P$)$: $14$ days

Using the Program Evaluation and Review Technique $($PERT$),$ calculate the expected duration and standard deviation for each task.