Problem $1$:

Consider the same project from Problem $1($i$.$e$.,$ the network diagram should look identical$).$ The

network diagram above is based on the most likely duration time for each activity. The table below

now provides additional information regarding the optimistic and pessimistic duration times.

$($a$)$ Determine the expected project completion time and the variance of the critical path using

expected time as duration. $($Hint: Compare the most likely time for each activity to the

duration in Problem $1\mathrm{.}2$ points$)$

Consider a path A$-$C$-$H for the following problems.

$($b$)$ Find the probability that the completion time of the path A$-$C$-$H will be $21$ weeks or more.

$(3$ points$)$

$($c$)$ Find the probability that the completion time of the path A$-$C$-$H will be $19$ weeks or more.

$(3$ points$)$

$($d$)$ Find the probability that the completion time of the path A$-$C$-$H will be $22$ weeks or less.

$(3$ points$)1.$ Consider the following network diagram for a project $($the times shown are in weeks$)$: