Total $=6$ points, part a $=3$ points; parts b $=2$ points and part c $1$ point.

Consider the following project. Use activity times as the most likely time for determining the critical path. Use the optimistic and pessimistic times $($together with activity times$)$ to determine expected completion time limits

a$.$ Draw PERT Chart with earliest and latest start and finish times$/$activity$.$ Fill in the slack time in the table for each activity. Show the slack time for each path for all paths and show Critical Path $($CPM$)$ and CPM time.

b$.$ What is the expected time for $68,95$ and $99$ percent Confidence Interval $($CI$)$ for the project?

c$.$ Show the $($ID $0=55\%,$ ID$1=60\%,$ ID $2=70\%,$ ID $3=80\%,$ ID $4=85\%,$ ID $5=50\%,$ ID $6=65\%,$ ID $7=75\%,8=99\mathrm{.}5\%,$ ID $9=97\mathrm{.}5\%),$ Confidence Interval for the project $($use section $7\mathrm{.}4\mathrm{.}3.$ page $225$ for parts $2/3)$ for only one percentage corresponding to your ID$,$ not all percentages.

$\backslash$table$[[$ID $0,$Preceeding,Start,End,Activity,Stafi,Optimistic,Pessimistic$],[$Activity$,$Activity,Node,Node,Time,Required,Time,Time$],[$A$,-,$S$,1,3,3,2,6],[$B$,-,$S$,2,2,2,1,3],[$C$,-,$S$,3,4,4,2,4],[$D$,$A B B$,1,4,3,3,3,5],[$E$,$B$,2,5,4,5,2,4],[$F$,$E$,5,$End,$2,3,4,5],[$G$,$C$,$ E$,3,$End,$4,4,2,6],[$H$,$D$,4,$End,$4,5,2,3]]$

Notes:

$2.$ This problem contains two Dummy activities.

$3.$ You can use Microsoft Project software for solution to this problem, but please show dummy activities in your solution.