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 takes more than 34 days? $\begin{array}{|l|l|l|l|l|}
\hline \text { Activity } & \begin{array}{l}
\text { Optimistic } \
\text { time }
\end{array} & \begin{array}{l}
\text { Most Likely } \
\text { time }
\end{array} & \begin{array}{l}
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & \text { - } \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline & & & & \text { Dig Holes, Plant } \
\text { Paint } & 9 & 11 & 13 & \text { Posts } \
\hline \text { Tack Wire } & 9 & 12 &16& \text { Weld Top Bar } \
\hline
\end{array}$

A)0.788
B)0.212
C)0.945
D)0.055

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 takes more than 34 days? $\begin{array}{|l|l|l|l|l|}
\hline \text { Activity } & \begin{array}{l}
\text { Optimistic } \
\text { time }
\end{array} & \begin{array}{l}
\text { Most Likely } \
\text { time }
\end{array} & \begin{array}{l}
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & \text { - } \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline & &  &  & \text { Dig Holes, Plant } \
 \text { Paint } & 9 & 11 & 13 & \text { Posts } \
\hline \text { Tack Wire } & 9 & 12 &16& \text { Weld Top Bar } \
\hline
\end{array}$

A)0.788
B)0.212
C)0.945
D)0.055

Quizplus · Accepted Answer

To calculate the probability that the project takes more than 34 days, we need to find the critical path and add up the time estimates of all the tasks on the critical path. From the table, we can see that the critical path is A-C-E-G, with a total time estimate of 36 days. Therefore, the probability of completing the project in more than 34 days is the probability of completing the critical path in more than 34 days. We can use a normal distribution with a mean of 36 days and a standard deviation of (4^2 + 2^2 + 4^2 + 4^2)^0.5 = 6 days (since task estimates are independent and can be added in quadrature). Using a standard normal distribution table or calculator, we can find that the probability of completing the critical path in more than 34 days is approximately 0.212. Therefore, the best choice is B.

A Gentleman Farmer Maniacally Works on Academic Projects to Raise