For the triangular distribution, we need only know or estimate the minimum, maximum, and most likely value. A project manager needs to estimate the time to complete the initial assessment for building a new corporate headquarters. From discussions with other experts, the manager believes six months is a best-case scenario and that 24 months is the worst-case scenario with 12 months being the most likely estimate. Those values define the triangular distribution below. When the graph loads, it displays the probability that completion time will be between 6 and 12 months. Drag on the graph to change the low and/or high values to compute the probability that the completion time will be between the low and high values. For example, drag the low and high ends so that the range is from 10 to 18 months. What is the probability completion time will be within that range?

0

5

10

15

20

25

x

P(6 <= x <=12) = 0.333

a. What is the probability that the completion time will be within 2 months of the most likely time to completion?

0.185

0.204

0.389

0.852

b. For what approximate completion time is there a 50/50 chance of exceeding?

12.0

13.6

15.0

16.7

c. The Company's upper management is considering providing a bonus for short completion times, but has determined that it is cost effective only when the bonus is provided for early completion times that have a 25% probability. For this project, the bonus should be provided if the completion time is at most what value?

11.2

12.0

15.0

16.7