The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances, as shown in the table. Graduation day is $16$ weeks from now. Assuming the project begins now, what is the probability that the project will be completed before

Graduation time?

The end of week $15?$

The end of week $13?$

Path

Expected Duration $($weeks$)$

Variance

A

$10$

$1\mathrm{.}21$

B

$8$

$2\mathrm{.}00$

C

$12$

$1\mathrm{.}00$

D

$15$

$2\mathrm{.}89$

E

$14$

$1\mathrm{.}44$