For a particular project, activities required to complete the project, the precedence relationships for the activities, and activity time estimates, as shown in the following table:

Activity Activity Predecessor Time Estimates $($Weeks$)$

a m b

A $-678$

B $-61218$

C $-$ $$357$

D B$,$ C $$6918$

E A$,$ B $5817$

F E$,$ D $101520$

G E$,$ F $5613$

a$.$ Draw the network diagram and show all calculations for ES$-$EF$-$LS$-$LF and Slack. You will have to find the expected time and variance for each activity.

b$.$ Identify the critical path by highlighting and find out the estimated project completion time, E$($T$)$ and the standard deviation for the project completion time, s

c$.$ Determine the probability that the project will be completed in $50$ weeks or less.