The manager of a local youth sports organization is planning its soccer season. The activities, their

immediate predecessors, and the activity time estimates $($in weeks$)$ are as follows.

Time $($weeks$)$

Activity Description Predecessor$($s$)$ Optim. Most Likely Pessim.

A Meet with board $1\mathrm{.}01\mathrm{.}52\mathrm{.}0$

B Interview$/$hire coaches A $3\mathrm{.}04\mathrm{.}06\mathrm{.}0$

C Reserve fields A $2\mathrm{.}03\mathrm{.}05\mathrm{.}0$

D Create schedule B$,$ C $1\mathrm{.}52\mathrm{.}02\mathrm{.}5$

E Meet with coaches B $2\mathrm{.}03\mathrm{.}04\mathrm{.}0$

F Register players A $1\mathrm{.}02\mathrm{.}04\mathrm{.}0$

G Order kits D $1\mathrm{.}02\mathrm{.}03\mathrm{.}0$

H Collect fees G $1\mathrm{.}02\mathrm{.}03\mathrm{.}0$

I Organize first practice E$,$ F$,$ H $0\mathrm{.}51\mathrm{.}02\mathrm{.}0$

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

$($b$)$ Compute the mean and variance of the duration of each activity. You may do this by hand or

by using technology, such as Excel.

$($c$)$ Determine the critical path, the expected project completion time, and the variance of the

project completion time.

$($d$)$ What is the probability that the planning process is completed within $12\mathrm{.}1$ weeks?

$($e$)$ What is the probability that the planning process takes longer than $14\mathrm{.}2$ weeks to complete?

$($f$)$ If the manager wants a $94\mathrm{.}5\%$ probability of completing the planning process on time, how far

ahead of the first practice should they start working?

MS $3053($Panda$)$ Problem Set #$10($Fall $2023)1$