$3)$ A company decides to plan a project, with activities, precedence relations and random duration statistics given in the following table:

Activity Immediate Predecessors Duration Minimum $($weeks$)$ Duration Mode $($weeks$)$ Duration Maximum $($weeks$)$

A none $259$

B A $168$

C A $3512$

D B $2412$

E B$,$ C $468$

F B $678$

G D$,$ E $126$

H F$,$ G $4616$

$$ Answer the following questions:

$3\mathrm{.}1)$ What method should be used? Compute the mean and variances for each activity and add them to the table above.

$3\mathrm{.}2)$ Draw the project network and label the arcs with the activity name.

$3\mathrm{.}3)$ Assuming that the critical path is A$-$B$-$P$1-$E$-$G$-$H$,$ compute the probability that this path duration is between $28$ weeks and $32$ weeks.

$3\mathrm{.}4)$ Assuming that the critical path is A$-$B$-$P$1-$E$-$G$-$H$,$ compute the number of weeks within which the project will be completed with probability $0\mathrm{.}95.$