For the project given below: how long is the project expected to take $($all values given are in weeks$)$ and what is the variance of the critical path? What is the probability the project will require $12$ weeks or less?

Immediate Optimistic Most Likely Pessimistic Activity Predecessors Time $($a$)$ Time $($m$)$ Time $($b$)$

$$A B C D E F$-$

A

A

A B$,$C$,$D E$1\mathrm{.}52\mathrm{.}50\mathrm{.}40\mathrm{.}51\mathrm{.}00\mathrm{.}52\mathrm{.}03\mathrm{.}50\mathrm{.}51\mathrm{.}03\mathrm{.}01\mathrm{.}05\mathrm{.}55\mathrm{.}50\mathrm{.}64\mathrm{.}58\mathrm{.}01\mathrm{.}5$