Q$5($Project Network PERT$)$The table below shows the preceding activities and PERT three$-$estimate times $($o $=$ optimistic; m $=$ most likely; p $=$ pessimistic$)$ that have been estimated for each activity to undertake a project. The times are in days. ActivityPredecessorompA$-3513$B$-23\mathrm{.}514$C$-135$DB$222$EB$129$FB$123$GC$111$HA$147$ID$135$JE$,$ F$0\mathrm{.}511\mathrm{.}5$KE$,$ I, J$12\mathrm{.}57$LG$,$ K$1413$a$)$For each activity, estimate the mean duration and variance. $[10$ marks$]$a$)$Draw an Activity on Node $($AoN$)$ network diagram to represent all activities. Complete the network diagram by putting in the activity durations; and calculate the activity times for all nodes. $[20$ marks$]$b$)$What is the critical path and the project duration?$[5$ marks$]$c$)$Calculate all the floats for each activities. Which activity floats are total float and which are independent float? Please comment and explain all your answers. $[10$ marks$]$d$)$What is the probability of completing in $20$ days? $[5$ marks$]$e$)$Determine the project duration with a risk of exceeding $20\%$