Answer this question with respect to the PERT problem posted in Canvas $($Test $10$ Output document above$).$ What is the variance of task $C?$

Management Science

PERT OUTPUT : The following estimates of activity times $($in days$)$ are available for a small project.

$\backslash$table$[[$Activity$,$Optimistic,Most Likely,Pessimistic$],[$A$,4,5,6],[$B$,8,9,10],[$C$,7,7\mathrm{.}5,11],[$D$,7,9,10],[$E$,6,7,9],[$F$,5,6,7]]$

Answering the following questions first will give you an early start for your test.

a$)$ Compute the expected completion time and variance for each activity.

b$)$ An analyst has determined that the project's critical path consists of B$-$D$-$F$.$ Compute the expected project completion time and standard deviation of project completion time.

c$)$ What is the probability that the project will complete before $27$ days?