$9\mathrm{.}13.$ Given the following network and probabilistic activity time estimates, determine the expected time and variance for each activity and indicate the critical path:A flow diagram shows the time estimates for different activities. The flow is as follows: a rectangular box labeled, Start, branches into three nodes: node $1,$ node $2,$ and node $3.$ Node $1$ leads to nodes $5,6,$ and $4$; nodes $2$ and $4$ lead to node $7$; node $3$ leads to nodes $8$ and $10$; node $5$ leads to node $9$; nodes $6,7,$ and $8$ lead to node $11$; and nodes $9,10,$ and $11$ lead to a rectangular box labeled, Finish.

The data under the nodes for different activities are shown as follows:

Node and number, activity number, activity time: a$,$ m$,$ and b$.$

Node $1$: Activity, $1$; Activity time, $6,10,15$;

Node $2$: Activity, $2$; Activity time, $2,7,16$;

Node $3$: Activity, $3$; Activity time, $4,8,11$;

Node $4$: Activity, $4$; Activity time, $3,10,15$;

Node $5$: Activity, $5$; Activity time, $7,9,20$;

Node $6$: Activity, $6$; Activity time, $4,12,15$;

Node $7$: Activity, $7$; Activity time, $3,6,9$;

Node $8$: Activity, $8$; Activity time, $5,9,16$;

Node $9$: Activity, $9$; Activity time, $3,20,25$;

Node $10$: Activity, $10$; Activity time, $4,12,16$;

Node $11$: Activity, $11$; Activity time, $2,9,14.$ActivityTime Estimates $($Weeks$)$amb$1610152271634811431015579206412157369859169320351041216112914$AnswerCP $=1-5-9=40\mathrm{.}33$ wk$,\backslash$alpha $=5\mathrm{.}9579\mathrm{.}14.$ What is the probability that the project in problem $9\mathrm{.}13$ will be completed in $35$ weeks? In $45$ weeks?