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 completing the project within 14 days, we need to find the critical path duration and the standard deviation of the project completion time.

Critical path duration = 6 + 5 + 4 = 15 days

To find the standard deviation, first, we need to find the variance of the critical path duration.

Variance = (6^2 + 5^2 + 4^2) = 77

Standard deviation = sqrt(variance) = sqrt(77) = 8.77

Now, we can use the normal distribution formula to calculate the probability of completing the project within 14 days, given a mean completion time of 15 days and a standard deviation of 8.77 days.

Z = (14 - 15) / 8.77 = -0.11

Using a standard normal distribution table or calculator, we find that the probability of completing the project within 14 days is approximately 0.023 or 2.3%. Therefore, the best answer choice is C.

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