The following table lists the activity time estimates $($in weeks$)$ for each activity.

Activity

Optimistic

Most Probable

Pessimistic

$5$

$6$

B

$2\mathrm{.}5$

$3$

$3\mathrm{.}5$

$7$

$8$

$9$

D

$5$

$5\mathrm{.}5$

$5$

$7$

$9$

F

$2$

$3$

$4$

G

$9$

$11$

H

$7$

$8$

$15$

Based only on the critical path, what is the estimated probability that the project will be completed with frame? $($Round your answers to four decimal places.$)$

$($a$)$ Within $21$ weeks?

$($b$)$

Within $23$ weeks?

$($c$)$

Within $27$ weeks?