$2-$For the following project

a$)$ Draw the network

b$)$ Calculate the expected time for each activity

c$)$ Calculate the ES$,$ EF$,$ LS$,$ LF$,$ the slack for each activity and identify the critical path

d$)$ Calculate the probability that the project will be completed by $13$ weeks.

e$)$ Calculate the probability that the project will be completed by $17$ weeks.

$\backslash$table$[[$Node Nos.,Predecessor$($s$),\backslash$table$[[$Shortest likely$],[$Time$]],\backslash$table$[[$Most likely$],[$Time$]],\backslash$table$[[$Longest Likely$],[$Time$]]],[1,----,1,2,3],[2,1,5,6,7],[3,1,3,4,5],[4,1,1,2,3],[5,2,2,4,6],[6,2,3,4,4,5,6],[7,2,1,3,5],[8,5,6,1,2,3]]$