Data for the following activities for The MSVU Project are below. The times are in weeks. The critical path for the project is A$-$D$-$H$-$I$-$J$-$K$.$ The expected completion time is $36\mathrm{.}5$ weeks. Determine the probability of completing the project by the $38$ week deadline. Ensure you show all your work including the variance calculations.

Activity

Optimistic Time

Most Likely Time

Pessimistic Time

A

$7$

$9$

$14$

B

$2$

$2$

$8$

C

$8$

$12$

$16$

D

$3$

$5$

$10$

E

$4$

$6$

$8$

F

$6$

$8$

$10$

G

$2$

$3$

$4$

H

$2$

$2$

$8$

I

$6$

$8$

$16$

J

$4$

$6$

$14$

K

$2$

$2$

$5$