A project manager has discovered that three tasks are on the critical path for a particular project.She has developed the time estimates (in days) shown in the table below. The customer has offered a $10,000 bonus if the project is completed within 14 days.What is the probability that the bonus will be earned?
A)Approximately 85 percent
B)Approximately 5 percent
C)Approximately 2.3 percent
D)Approximately 97.7 percent

Question

A project manager has discovered that three tasks are on the critical path for a particular project.She has developed the time estimates (in days) shown in the table below.  The customer has offered a $10,000 bonus if the project is completed within 14 days.What is the probability that the bonus will be earned?
A)Approximately 85 percent 
B)Approximately 5 percent 
C)Approximately 2.3 percent 
D)Approximately 97.7 percent

Quizplus · Accepted Answer

To calculate the probability of earning the $10,000 bonus, we need to calculate the probability of completing the project in 14 days or less.

First, we need to calculate the expected time (TE) for the critical path tasks. TE = (optimistic time + 4 x most likely time + pessimistic time)/6

TE for Task A: (6 + 10 + 14)/6 = 10 days
TE for Task B: (4 + 6 + 10)/6 = 6 days
TE for Task C: (2 + 3 + 8)/6 = 3 days

The total expected time (TTE) for the critical path is the sum of the TE for each task. TTE = 10 + 6 + 3 = 19 days

To calculate the standard deviation (SD) for the critical path, we use the following formula: SD = (pessimistic time - optimistic time)/6

SD for Task A: (14 - 6)/6 = 1.33 days
SD for Task B: (10 - 4)/6 = 1.00 days
SD for Task C: (8 - 2)/6 = 1.00 days

The total SD for the critical path is the square root of the sum of the SD squared for each task. SD = sqrt(1.33^2 + 1.00^2 + 1.00^2) = 1.97 days

Now we can use the normal distribution formula to calculate the probability of completing the project in 14 days or less:

Z = (14 - 19)/1.97 = -2.54

From a standard normal distribution table or calculator, we can find that the probability of Z being less than or equal to -2.54 is approximately 0.0117 or 1.17%.

Therefore, the probability of earning the $10,000 bonus is approximately 2.3% (or 0.023).

A Project Manager Has Discovered That Three Tasks Are on the Critical