Part $1$: Using the information given,

a$)$ Calculate the completion time of the project.

b$)$ Identify the activities on the critical path.

Activity Normal Time

$($weeks$)$

A $4$

B $3$

C $5$

D $2$

E $5$

F $6$

G $4$

H $3$

Part $2$: Using the table below, calculate the expected time for activity and the variance of estimated time for activity for activities A$-$B$.$

Activity

Optimistic Time Most Likely Time

Pessimistic Time

Expected Time

$\backslash$sigma $2$

A $138$

B $245$

Part $3$:

The following interior activities need to be completed before the new Oil Slick auto service store can be opened. The contractor is not sure when all the work will be done, but was able to come up with the following estimates $($in days$).$

Activity predecessor optimistic time most likely time pessimistic time

A $($install floor$)-----468$

B $($paint$)$ A $151719$

C $($install signs$)$ B $41220$

D $($final cleaning$)$ C $6810$

If all these remaining activities are critical, what would be the expected completion time, in days, of the remainder of the project? Path $($A$,$B$,$C$,$D$)$