$..3\mathrm{.}17$ Thabo Mbeki, president of Mbeki Construction, has developed the tasks, durations, and predecessor relationships in the following table for building new motels. Draw the AON network and answer the questions that follow.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$($s$]],$Time Estimates $($in weeks$)],[$Optimisti$,\backslash$table$[[$Most$],[$Likely$]],$Pessimistic$],[$A$,+1,4,8,10],[$B$,$A$,2,8,24],[$C$,$A$,8,12,16],[$D$,$A$,4,6,10],[$E$,$B$,1,2,3],[$F$,E,C,6,8,20],[$G$,E,C,2,3,4],[$H$,$F$,2,2,2],[1,$F$,6,6,6],[$I$,$D$,$ G$,$ H$,4,6,12],[$K$,$I. J$,2,2,3]]$

a$)$ What is the expected $($estimated$)$ time for activity C$??$

b$)$ What is the variance for activity C$?$

c$)$ Based on the calculation of estimated times, what is the critical path?

d$)$ What is the estimated time of the critical path?

e$)$ What is the activity variance along the critical path?

f$)$ What is the probability of completion of the project before week $36?$