Suppose that the following estimates of activity times $($in weeks$)$ were provided for the network shown above.

Activity Optimistic Most Probable Pessimistic

A $4\mathrm{.}05\mathrm{.}06\mathrm{.}0$

B $2\mathrm{.}53\mathrm{.}03\mathrm{.}5$

C $6\mathrm{.}07\mathrm{.}08\mathrm{.}0$

D $5\mathrm{.}05\mathrm{.}59\mathrm{.}0$

E $5\mathrm{.}07\mathrm{.}09\mathrm{.}0$

F $2\mathrm{.}03\mathrm{.}04\mathrm{.}0$

G $8\mathrm{.}010\mathrm{.}012\mathrm{.}0$

H $6\mathrm{.}07\mathrm{.}014\mathrm{.}0$

What is the probability that the project will be completed within the following time frames? $($Round your answers to four decimal places. You may need to use the appropriate technology to answer this question.$)$

$($a$)$

Within $19$ weeks?

$($b$)$

Within $22$ weeks?

$($c$)$

Within $23$ weeks?