Question $2$:

Using Table$1$ and the results of Question $1,$ answer the following questions

What is the probability of completing the project in $95$ days? $(6$ pnt$)$

How many days are needed to complete the project with $97\%$ certainty? $(6$ pnt$)$

If we want to achieve $98\%$ certainty, how many days should be allocated for the project? $(6$ pnt$)$

Show all your work and explain your reasoning for each step.

Question $3$:

Using the AOA analysis, answer the following questions:

Calculate the expected duration $($TE$)$ for each activity using the PERT formula: $(a+4m+$ b$)/6(6$ pnt$)$

Determine the critical path of the project. $(4$ pnt$)$

Draw the network as AOA $(10$ pnt$)$

Calculate the Early Start $($ES$),$ Early Finish $($EF$),$ Late Start $($LS$),$ and Late Finish $($LF$)$ for each activity. $(8$ pnt$)$

Calculate the slack time for each activity. $(4$ pnt$)$

What is the expected completion time for the entire project? $(5$ pnt$)$

Determine the certainty of finishing the project in $37$ days. $(5$ pnt$)$

If we want to achieve $95\%$ certainty, how many days should be allocated for the project? $(4$ pnt$)$

If we want to achieve $99\%$ certainty, how many days should be allocated for the project? $(4$ pnt$)$

Show all your work and explain your reasoning for each step.

Table $2-$Question $3$

$\backslash$table$[[$Activity$,$Description,$\backslash$table$[[$Optimistic$],[$Time $($a$)]],\backslash$table$[[$Most$],[$Likely$],[$Time $($m$)]],\backslash$table$[[$Pessimistic$],[$Time $($b$)]],\backslash$table$[[$Preceding$],[$Event$]],\backslash$table$[[$Succeeding$],[$Event$]]],[$A$,\backslash$table$[[$Requirements$],[$Gathering$]],3,5,7,1,2],[$B$,$System Design,$6,8,10,2,3],[$C$,\backslash$table$[[$Database$],[$Development$]],4,6,8,2,4],[$D$,\backslash$table$[[$Frontend$],[$Development$]],7,9,11,3,5],[$E$,\backslash$table$[[$Backend$],[$Development$]],8,10,12,4,5],[$F$,\backslash$table$[[$Integration$]],3,5,7,5,6],[$G$,$Testing,$5,7,9,6,7],[$H$,$Deployment,$2,3,4,7,8]]$