$($All answers were generated using $1,000$ trials and native Excel functionality.$)$

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 diagram shows the precedence relationship in the project. Activities are labeled from A to G$.$ Activities A and B can be started after the start of the project. Activity C can be started after completion of activity A$.$ Activity E can be started after comletion of activities C and B$.$ Activity G can be started after completion of activity E$.$ Activity D can be started after completion of activity B$.$ Activity F can be started after completion of activity D$.$ The project can be finished after completion of activities F and G$.$

$($a$)$Using the triangular distribution to represent the duration of each activity, construct a simulation model to estimate the average amount of time to complete the concert preparations.Round your answers to one decimal place.

Project Duration Average days Standard Deviation days

$($b$)$What is the likelihood that the project will be complete in $23$ days or less?Round your answer to the nearest whole number.