Homework Problem $1\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}\backslash$hline Activity & Predecessor & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$ Duration $\}\backslash \backslash \backslash$cline $\{2-5\}$ & & Optimistic & Most Likely & Pessimistic $\backslash \backslash \backslash$hline A & $-$ & $2$ & $4$ & $12\backslash \backslash \backslash$hline B & $-$ & $10$ & $12$ & $26\backslash \backslash \backslash$hline C & A & $8$ & $9$ & $10\backslash \backslash \backslash$hline D & A & $10$ & $15$ & $20\backslash \backslash \backslash$hline E & A & $7$ & $7\mathrm{.}5$ & $11\backslash \backslash \backslash$hline F & B$-$C & $9$ & $9$ & $9\backslash \backslash \backslash$hline G & D & $3$ & $3\mathrm{.}5$ & $7\backslash \backslash \backslash$hline H & E$,$ E$,$ G & $5$ & $5$ & $5\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$ Considering the Project Details; $1.$ Construct the Project Network Diagram $2.$ Find the Expected Duration and Standard Deviation and Variance of each Activity $3.$ Find the Critical path and Expected Project Completion Time $4.$ If the project due date is $30$ weeks, what is the probability of meeting the due date? $5.$ What should be the scheduled completion time for the probability of completion to be

$80\%$