The following information is given below about a project.

$\backslash$table$[[$Activity$,$Optimistic Time $($weeks$),\backslash$table$[[$Most$],[$Likely$],[$Time$],[($weeks$)]],$Pessimistic Time $($weeks$),$Expected Time $($weeks$),$Variance,$\backslash$table$[[$Immediate$],[$Predecessor$($s$)]]],[,$a$,$m$,$b$,$t$,{}^2,],[$A$,4,7,10,,,$A$],[$B$,2,8,20,,,$A$],[$C$,8,12,16,,,,$A$],[$D$,1,2,3,,,$B$],[$E$,6,8,22,,,-$ D$,$ C$],[$F$,2,3,4,,,$C$],[$G$,2,2,2,,,$F$],[$H$,6,8,10,,,],[$I$,4,8,12,,,$E$,5,$ H$],[$J$,1,2,3,-,,$I$]]$

a$.$ Determine the expected activity time $(t)$ and variance $({}^2)$ for each activity. Draw the network diagram using the expected times and the precedence information in the above table.

b$.$ Determine the Earliest Start $($ES$),$ Earliest Finish $($EF$),$ Latest Start $($LS$),$ Latest Finish $($LF$),$ and Slack values for each activity, and complete the table below.

$\backslash$table$[[$Activity$,\backslash$table$[[$Earliest$],[$Start$]],\backslash$table$[[$Earliest$],[$Finish$]],\backslash$table$[[$Latest$],[$Start$]],\backslash$table$[[$Latest$],[$Finish$]],$Slack$],[$A$,,,,,],[$B$,,,,,],[$C$,,,,,],[$D$,,,,,],[$E$,,,,,],[$F$,,,,,],[$G$,,,,,],[$H$,,,,,],[$I$,,,,,],[$J$,,,,,]]$

c$.$ Determine the critical path for this project. Calculate the expected project duration and standard deviation. Then use the z$-$score table attached on the next page of this assignment to determine the probability that the