QUESTION TWO

$[30]$

The estimated times for a project that you are working on is listed in the table below:

$\backslash$table$[[$ACTIVITY$,$PREDECESSOR,$\backslash$table$[[$MOST OPTIMISTIC$],[($DAYS$)]],\backslash$table$[[$MOST LIKELY$],[($DAYS$)]],\backslash$table$[[$MOST PESSIMISTIC$],[($DAYS$)]]],[$A$,-,6,9,16],[$B$,$A$,11,15,20],[$C$,$A$,2,6,10],[$D$,$B$,10,12,15],[$E$,$B$,2,5,6],[$F$,$C$,4,6,12],[$G$,$E;F$,6,9,14],[$H$,$D;E$,3,7,9],[$I$,$H;G$,3,6,]]$

$2\mathrm{.}1$ Using the PERT formula, calculate the time $($t$)$ value for each activity. Please round off days i$.$e$.$ no decimal places.

$(5)$

$2\mathrm{.}2$ Calculate the variance $($v$)$ for each activity. Please use $2$ decimal places.

$(5)$

$2\mathrm{.}3$ Construct the network diagram $($Activity on Node $-$ AON$).$

$(15)$

$2\mathrm{.}4$ Calculate the probability of this project being completed in $55$ days.

$(5)$