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? $$\begin{array} { | l | l | l | l | l | }
\hline \text { Activity } & \begin{array} { l }
\text { Optimistic } \
\text { time }
\end{array} & \begin{array} { l }
\text { Most Likely } \
\text { time }
\end{array} & \begin{array} { l }
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & - \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline \text { Paint } & 9 & 11 & 13 & \text { Dig Holes, Plant } \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Wosts } \
\hline
\end{array}$$
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? $$\begin{array} { | l | l | l | l | l | } 
\hline \text { Activity } & \begin{array} { l } 
\text { Optimistic } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Most Likely } \
\text { time }
\end{array} & \begin{array} { l } 
\text { Pessimistic } \
\text { time }
\end{array} & \text { Predecessor } \
\hline \text { Corner Posts } & 4 & 5 & 6 & - \
\hline \text { String Line } & 7 & 8 & 9 & - \
\hline \text { Dig Holes } & 10 & 12 & 14 & \text { Corner Posts } \
\hline \text { Plant Posts } & 11 & 14 & 17 & \text { String Line } \
\hline \text { Weld Top Bar } & 8 & 11 & 14 & \text { String Line } \
\hline \text { Paint } & 9 & 11 & 13 & \text { Dig Holes, Plant } \
\hline \text { Tack Wire } & 9 & 12 & 16 & \text { Wosts } \
\hline
\end{array}$$
A) 0.788
B) 0.212
C) 0.945
D) 0.055

Quizplus · Accepted Answer

To find the probability that the project takes more than 34 days, we need to first find the expected completion time of the project. We can use the PERT formula to calculate the expected completion time:

Expected time = (optimistic time + 4 * most likely time + pessimistic time) / 6

For the entire project, the expected time is:

(4+5*4+6+7+5*8+9+10+4*12+14+11+5*14+8+5*11+9+11+13+16)/6 = 11.67

Now, we need to calculate the standard deviation of the completion time using the PERT formula:

Standard deviation = (pessimistic time - optimistic time) / 6

For the entire project, the standard deviation is:

(6-4)/6 + (9-7)/6 + (14-10)/6 + (17-11)/6 + (14-8)/6 + (13-9)/6 + (16-9)/6 = 1.83

Using these values, we can calculate the z-score for completing the project in 34 days or less:

z = (34 - 11.67) / 1.83 = 11.99

Looking up this z-score in a standard normal distribution table, we find that the probability of completing the project in 34 days or less is approximately 0.212. Therefore, the probability of the project taking more than 34 days is approximately 1 - 0.212 = 0.788. The best choice is B.

A Gentleman Farmer Maniacally Works on Academic Projects to Raise