$*3\mathrm{.}21$ Rich Cole Control Devices, Inc., produces custombuilt relay devices for auto makers. The most recent project undertaken by Cole requires $14$ different activities. Cole's managers would like to determine the total project completion time $($in days$)$ and those activities that lie along the critical path. The appropriate data are shown in the following table.

a$)$ What is the probability of being done in $53$ days?

b$)$ What date results in a $99\%$ probability of completion?

$\backslash$table$[[$Ac$$m:$,,,\backslash$table$[[$Most$],[$LKELY$],[$TME$]],\backslash$table$[[$PESSIMISTIC$],[$TIME$]]],[$A$,-1,4,6,7],[8,-,1,2,3],[$C$,$A$,6,6,6],[$D$,$A$,5,8,11],[$E$,$B$.$C$,1,9,18],[$F$,$D$,2,3,6],[6,$D$,1,7,8],[$H$,$E$,$ F$,4,4,6],[1,$G$.$ H$,1,6,8],[$J$,1,2,5,7],[$K$,1,8,9,11],[$L$,$J$,2,4,6],[$M$,$K$,1,2,3],[N,$L$.,$ M$,6,8,10]]$