At a local university, the Student Commission on Programming and Entertainment $($SCOPE$)$ is preparing to host its first music concert of the school year. To successfully produce this music concert, SCOPE has to complete several activities. The following table lists information regarding each activity. An activity's immediate predecessors are the activities that must be completed before the considered activity can begin. The table also lists duration estimates $($in days$)$ for each activity.

ActivityImmediate

PredecessorsMinimum

TimeLikely

TimeMaximum

TimeA: Negotiate contract with selected musicians$-569$B: Reserve site$-81215$C: Logistical arrangements for music groupA$567$D: Screen and hire security personnelB$333$E: Advertising and ticketingB, C$159$F: Hire parking staffD$4710$G: Arrange concession salesE$3810$

The following network illustrates the precedence relationships in the SCOPE project. The project begins with activities A and B$,$ which can start immediately $($time $0)$ because they have no predecessors. On the other hand, activity E cannot be started until activities B and C are both completed. The project is not complete until all activities are completed.

A network with $9$ nodes is shown. The node labeled "Start" points to $2$ nodes labeled $"$A$"$ and $"$B$."$ The node labeled $"$A$"$ points to the node labeled $"$C$,""$C$"$ points to the node labeled $"$E$,""$E$"$ points to the node labeled $"$G$,",$ and $"$G$"$ points to the node labeled "Finish." The node labeled $"$B$"$ points to $"$E$"$ and the node labeled $"$D$,""$D$"$ points to the node labeled $"$F$,"$ and $"$F$"$ points "Finish."

$($a$)$

Using the triangular distribution to represent the duration of each activity, construct a simulation model to estimate the average amount of time $($in days$)$ to complete the concert preparations. $($Use at least $1,000$ trials. Round your answer to one decimal place.$)$

days

$($b$)$

What is the likelihood that the project will be complete in $23$ days or less? $($Use at least $1,000$ trials. Round your answer to three decimal places.$)\backslash$begin$\{$tabular$\}\{|$l$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multicolumn$\{1\}\{|$c$|\}\{$ Activity $\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Immediate $\backslash \backslash$

Predecessors

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Minimum $\backslash \backslash$

Time

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Likely $\backslash \backslash$

Time

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Maximum $\backslash \backslash$

Time

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

$\backslash$hline A: Negotiate contract with selected musicians & $-$ & $5$ & $6$ & $9\backslash \backslash$

$\backslash$hline B: Reserve site & $-$ & $8$ & $12$ & $15\backslash \backslash$

$\backslash$hline C: Logistical arrangements for music group & A & $5$ & $6$ & $7\backslash \backslash$

$\backslash$hline D: Screen and hire security personnel & B & $3$ & $3$ & $3\backslash \backslash$

$\backslash$hline E: Advertising and ticketing & B$,$ C & $1$ & $5$ & $9\backslash \backslash$

$\backslash$hline F: Hire parking staff & D & $4$ & $7$ & $10\backslash \backslash$

$\backslash$hline G: Arrange concession sales & E & $3$ & $8$ & $10\backslash \backslash$

$\backslash$hline

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

activities B and C are both completed. The project is not complete until all activities are completed. decimal place.$)$

$\backslash (\backslash$square $\backslash )$

$\backslash [$

x $\backslash$text $\{$ days $\}$

$\backslash ]$

$($b$)$ What is the likelihood that the project will be complete in $23$ days or less? $($Use at least $1,000$ trials. Round your answer to three decimal places.$)$