CAMMIMS$169.$E$\mathrm{.}018.$

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Due to population growth in the area, the new Liberty High School has just opened in a local school district. The athletic director at Liberty High is planning the launch of the school's track and field team. The first team practice is scheduled for April $1.$ The activities, their immediate predecessors, and the activity time estimates $($in weeks$)$ are listed in the following table.

$\backslash$table$[[$Activity$,$Description,$\backslash$table$[[$Immediate$],[$Predecessor$]],$Optimistic,Most Probable,Pessimistic$],[$A$,$Meet with board,,$1,1,2],[$B$,$Hire coaches,A$,4,6,8],[$C$,$Conduct fundraiser,A$,2,4,6],[$D$,$Announce program,B$,$ C$,1,2,3],[$E$,$Meet with coaches,B$,2,3,4],[$F$,$Order team equipment,A$,1,2,3],[$G$,$Register athletes,D$,1,2,3],[$H$,$Reserve buses for meets,G$,1,2,3],[$I$,$Plan first practice,E$,$ H$,$ F$,1,1,1]]$

$($a$)$ Draw a project network.

$(1)$

$($b$)$ Develop an activity schedule. $($Round your answers to two decimal places.$)$

$\backslash$table$[[$Activity$,\backslash$table$[[$Earliest$],[$Start$]],\backslash$table$[[$Latest$],[$Start$]],\backslash$table$[[$Earliest$],[$Finish$]],\backslash$table$[[$Latest$],[$Finish$]],$Slack$],[$A$,,,,,],[$B$,,,,,],[$C$,,,,,],[$D$,,,,,],[$E$,,,,,],[$F$,,,,,],[$G$,,,,,],[H,,,,,],[$I$,,,,,]]$

$($c$)$ What are the critical activities? $($Enter your answers as a comma$-$separated list.$)$

What is the expected project completion time $($in weeks$)?($Round your answer to two decimal places.$)$ weeks

$($d$)$ If the athletic director plans to start the project on January $1,$ calculate the probability the track and field team will be ready by the scheduled April $1$ date $(13$ weeks$)$ based solely on the critical path. $($Round your answer to four decimal places.$)$

Should the athletic director begin planning the track and field team before January $1?($The probability for finishing on schedule should be at least $0\mathrm{.}9.)$

Since the probability that the track and field team will be ready by April $1$ is $---$Select$--$ hat$(v)$ than $0\mathrm{.}9,$ the athletic director $---$Select$--$ diamond begin planning before January $1.$

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