You may need to use the appropriate technology to answer this question.

The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon's management learned that a competitor is working to introduce a similar product. As a result, Landon's top management increased its pressure on the product development group. The group's leader turned to PERT$/$CPM as an aid to scheduling the activities remaining before the new product can be brought to the market.

The project network is depicted in the following diagram.

The activity time estimates $($in weeks$)$ are listed in the following table.

$\backslash$table$[[$Activity$,$Optimistic,Most Probable,Pessimistic$],[$A$,3,4,5],[$B$,3,3\mathrm{.}5,7]]$

$\backslash$table$[[$C$,4,5,6],[$D$,2,3,4],[$E$,5,10,15],[$F$,6\mathrm{.}5,7\mathrm{.}5,11\mathrm{.}5],[$G$,4\mathrm{.}5,6,7\mathrm{.}5],[$H$,6,7,14],[$I$,2,2\mathrm{.}5,6],[$J$,4,5,6]]$

$($a$)$ Develop an activity schedule for this project and identify the critical path activities. $($Enter your answers as a comma$-$separated list.$)$

$($b$)$ Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within $25$ weeks? $($Round your answer to four decimal places.$)$

$($c$)$ Based solely on the critical path, what is the probability that the project will be completed so that Landon Corporation may introduce the new product within $31$ weeks? $($Round your answer to four decimal places.$)$