A gentleman farmer maniacally works on academic projects to raise funds for his true passion,farming.He has identified seven tasks and developed three time estimates (all in days)of the next big project on the farm,replacing the fence at the comedy pasture.Tasks,precedence requirements,and time estimates are shown in the table.What is the probability that the project is completed in 31 days? $$\begin{array} { | l | l | l | l | l | }
\hline \text { Activity } & \begin{array} { l }
\text { Optimistic } \
\text { time }
\end{array} & \begin{array} { l }
\text { Most Likely } \
\text { time }
\end{array} & \begin{array} { l }
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & - \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline \text { Paint } & 9 & & & \text { Dig Holes, Plant } \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Posts } \
\hline
\end{array}$$
A) 0.055
B) 0.092
C) 0.125
D) 0.187

Question

A gentleman farmer maniacally works on academic projects to raise funds for his true passion,farming.He has identified seven tasks and developed three time estimates (all in days)of the next big project on the farm,replacing the fence at the comedy pasture.Tasks,precedence requirements,and time estimates are shown in the table.What is the probability that the project is completed in 31 days? $$\begin{array} { | l | l | l | l | l | } 
\hline \text { Activity } & \begin{array} { l } 
\text { Optimistic } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Most Likely } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & - \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline \text { Paint } & 9 & & & \text { Dig Holes, Plant } \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Posts } \
\hline
\end{array}$$
A) 0.055
B) 0.092
C) 0.125
D) 0.187

Quizplus · Accepted Answer

The correct answer is A.The critical path is Corner Posts - String Line - Dig Holes - Plant Posts - Tack Wire, with a total duration of 31 days. The probability of completing the project in 31 days is the probability that all activities on the critical path are completed in their most likely times. This probability is 0.055.

A Gentleman Farmer Maniacally Works on Academic Projects to Raise