MS $3053-$ Problem Set $\backslash$#$10$

Due Date: December $3,2024$

$\backslash$#$1$

The manager of a local sports club is planning its soccer season. The activities, their immediate predecessors, and the activity time estimates $($in weeks$)$ are as follows.

$($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 duration, and the variance of the project duration.

$($d$)$ What is the probability that the planning process is completed within $13\mathrm{.}9$ weeks?

$($e$)$ What is the probability that the planning process takes longer than $12\mathrm{.}4$ weeks?

$($f$)$ If the manager wants a $\backslash (92\mathrm{.}5\backslash \%\backslash )$ probability of completing the planning process on time, how far ahead of the first practice should they start the project?