Use the network diagram and the table to answer the following questions:

$\backslash$table$[[$ACTIVITY$,$OPTIMISTIC,$\backslash$table$[[$MOST$],[$LIKELY$]],$PESSIMISTIC,$\backslash$table$[[$EXPECTED$],[$TIME$]],$VARIANCE$],[$A$,1,2\mathrm{.}5,,,0\mathrm{.}25],[$B$,$N$/$A$,$N$/$A$,$N$/$A$,3,0\mathrm{.}5],[$C$,$N$/$A$,$N$/$A$,$N$/$A$,5,0\mathrm{.}7],[$D$,$N$/$A$,$N$/$A$,$N$/$A$,6,0\mathrm{.}6],[$E$,$N$/$A$,$N$/$A$,$N$/$A$,2,0\mathrm{.}6],[$F$,$N$/$A$,$N$/$A$,$N$/$A$,4\mathrm{.}5,0\mathrm{.}4],[G,$N$/$A$,$N$/$A$,$N$/$A$,2,0\mathrm{.}8],[H,2,5,8,,]]$

a$.$ Fill the empty cells in the diagram and table.

b$.$ What is the critical path?

c$.$ What is the expected project completion time?

d$.$ What is the variance of project completion time?

e$.$ What is the probability that this project can be completed in $16$ or fewer days?

f$.$ What is the probability that this project would be completed in more than $19$ days?