$*3\mathrm{.}23$ Using PERT, Adam Munson was able to determine that the expected project completion time for the construction of a pleasure yacht is $21$ months, and the project variance is $4.$

a$)$ What is the probability that the project will be completed in $17$ months?

b$)$ What is the probability that the project will be completed in $20$ months?

c$)$ What is the probability that the project will be completed in $23$ months?

d$)$ What is the probability that the project will be completed in $25$ months?

e$)$ What is the due date that yields a $95\%$ chance of completion?

$-3\mathrm{.}29$ What is the minimum cost of crashing the following project that Roger Solano manages at Slippery Rock University by $4$ days?

$\backslash$table$[[$ACTIVITY$,\backslash$table$[[$NORMAL$],[$TIME$],[($DAYS$)]],\backslash$table$[[$CRASH$],[$TIME$],[($DAYS$)]],\backslash$table$[[$NORMAL$],[$COST$]],\backslash$table$[[$CRASH$],[$COST$]],\backslash$table$[[$IMMEDIATE$],[$PREDECESSOR$($S$)]]],[$A$,6,5,$$$900,$$$1,000,-],[$B$,8,6,300,400,-],[$C$,4,3,500,600,-],[$D$,5,3,900,1,200,$A$],[$E$,8,5,1,000,1,600,$C$]]$