$\backslash$table$[[,$DAYS,IMMEDIATE,$],[$ACTIVITY$,a,m,b,$PREDECESSORS$],[$A$,3,6,9,-],[$B$,2,4,6,-],[$C$,1,2,3,-],[$D$,6,7,8,$C$],[$E$,2,4,6,$B$,$ D$],[$F$,6,10,14,$A$,$ E$],[$G$,1,2,6,$A$,$ E$],[$H$,3,6,9,$F$],[$I$,10,11,12,$G$],[$J$,14,16,21,$G$],[$K$,2,8,11,$H$,$ I$]]$

$($a$)$ Develop a project network for this problem.

$($b$)$ Determine the expected duration and variance for each activity.

$($c$)$ Determine the ES$,$ EF$,$ LS$,$ LF$,$ and slack time for each activity. Also determine the total project completion time and critical path$($s$).$

$($d$)$ What is the probability that this job will finish in $38$ days or less?