Problem $3.($PERT for risk management.$)$ Consider this project network.

The following table shows $a,m,b($in days$)$ for each activity of the project.

Please answer the following questions.

Compute $t_e($expectation$),($standard deviation$)$ and $V($variance$)$ of the duration of each

activity. $($Note: Keep one decimal place after the dot in your result.$)$

Identify the critical path by visual inspection.

$($Hint: there are total $4$ paths from start to end.$)$

The critical path$($s$)$ is:

$($In case of multiple critical paths, pick one to continue.$)$

Compute $T_e($expectation$)$ and $V_P($variance$)$ of the duration of the project.

$($Note: keep one decimal place after the dot in your result.$)$

What's the probability that the project is completed within $28$ days.

For what project due date $($denoted as $TS)$ is the project to be completed on time with

$95\%$ chance?