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:

$\backslash$table$[[,$Activity,Time Estimates $($Weeks$)],[$Activity$,$Predecessor,a$,$m$,$b$,],[$A$,-,6,7,8,],[$B$,-,6,12,18,],[$C$,-,3,5,7,],[$D$,$B$,$ C$,6,9,18,],[$E$,$A$,$ B$,5,8,17,],[$F$,$E$,$ D$,10,15,20,],[$G$,$E$,$ F$,5,6,13,]]$

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.

d$.$ What is the probability that the project will take more than $40$ week