To help with preparations, a couple has devised a project network to describe the activities that must be completed by their wedding date.

A project network with $10$ activities and $13$ directed arcs is shown.

Activity Start is connected to activity A and to activity B$.$

Activity A is connected to activity C and to activity D$.$

Activity B is connected to activity E$.$

Activity C is connected to activity H$.$

Activity D is connected to activity F and to activity G$.$

Activity E is connected to activity F and to activity G$.$

Activity F is connected to activity H$.$

Activity G is connected to activity Finish.

Activity H is connected to activity Finish.

Activity Finish has no arcs directed to other activities.

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

Activity Optimistic Most Probable Pessimistic A$456$ B$2\mathrm{.}533\mathrm{.}5$ C$567$ D$55\mathrm{.}59$ E$579$ F$234$ G$91113$ H$7815$

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

$($a$)$

Within $21$ weeks?

$($b$)$

Within $23$ weeks?

$($c$)$

Within $27$ weeks? You may need to use the appropriate technology to answer this question.

To help with preparations, a couple has devised a project network to describe the activities that must be completed by their wedding date.

i$)$

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

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Activity & Optimistic & Most Probable & Pessimistic $\backslash \backslash$

$\backslash$hline A & $4$ & $5$ & $6\backslash \backslash$

$\backslash$hline B & $2\mathrm{.}5$ & $3$ & $3\mathrm{.}5\backslash \backslash$

$\backslash$hline C & $7$ & $8$ & $9\backslash \backslash$

$\backslash$hline D & $5$ & $7\mathrm{.}5$ & $9\backslash \backslash$

$\backslash$hline E & $5$ & $3$ & $4\backslash \backslash$

$\backslash$hline F & $2$ & $9$ & $15\backslash \backslash$

$\backslash$hline G & $7$ & $8$ & $9\backslash \backslash$

$\backslash$hline H & $7$ & & $9\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

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

$($b$)$ Within $23$ weeks?

$($c$)$ Within $27$ weeks?