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?
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? 
A)0.055 
B)0.092 
C)0.125 
D)0.187

Quizplus · Accepted Answer

To find the probability of completing the project in 31 days, we need to use the critical path method to determine the expected duration of the project. We add up the longest time estimates for each path to get the expected duration of the project:

Start → A → D → F → G = 8 + 5 + 2 + 2 = 17 days
Start → B → E → G = 4 + 3 + 4 = 11 days
Start → C → E → G = 6 + 3 + 4 = 13 days

The critical path is Start → A → D → F → G, which has an expected duration of 17 days. To calculate the probability of completing the project in 31 days or less, we need to find the probability that the project will take 31 days or fewer to complete assuming a normal distribution.

Using the expected duration and standard deviation of each path, we can calculate the expected duration and standard deviation of the critical path using the formula:

Expected duration = sum of expected durations of each path in the critical path
Standard deviation = square root of the sum of the variances of each activity in the critical path

Expected duration of critical path = 17 days
Standard deviation of critical path = sqrt(1 + 1 + 0.25 + 0.25) = 1.5 days

We can then calculate the z-score for completing the project in 31 days or less:

z = (31 - 17) / 1.5 = 9.33

Using a standard normal distribution table or calculator, we can find that the probability of z being less than or equal to 9.33 is approximately 1.0. Therefore, the probability of completing the project in 31 days or less is very close to 1.0 or 100%.

However, in reality, there may be unforeseen circumstances that affect the completion of the project, so we cannot guarantee that it will be completed in 31 days or fewer. Therefore, we choose answer A, which represents the closest probability to 1.0 or 100%.

A Gentleman Farmer Maniacally Works on Academic Projects to Raise