A new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks.

A new project is to be completed. The following activities need to be completed in the order shown, where times are in weeks.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$predecessors$]],\backslash$table$[[$Optimistic$],[$time$]],\backslash$table$[[$Most$],[$likely$],[$time$]],\backslash$table$[[$Most$],[$pessimistic$],[$time$]],$Variance$],[$A$,-,2,3,4,0\mathrm{.}11111],[$B$,-,2,4,6,0\mathrm{.}44444],[$C$,$A$,$B$,1,2,3,0\mathrm{.}11111],[$D$,$B$,1,3,5,0\mathrm{.}44444],[$E$,$A$,2,3,4,0\mathrm{.}11111],[$F$,$C$,1,4,7,1],[$G$,$E$,$F$,2,2,2,0],[$H$,$D$,$F$,2,5,8,1],[$I$,$G$,$H$,1,3,5,0\mathrm{.}44444],[$J$,$I,$2,3,4,0\mathrm{.}11111]]$ a$)$Determine and state the critical path for this project.

$($b$)$ What are the expected time and the variance of the project?

$($c$)$ What is the probability that the project is completed in $22$ or fewer weeks

$($d$)$ What date should be set such that there is a $94\%$ chance of completion within that time?