56. A new project manager in a construction company was helping prepare the duration estimates for a house rehabilitation project. The project manager was working with the lead estimator who said the company uses the triangular distribution method to determine activity durations. Based on the estimator's experience, the project could take as long as 1,500 labor hours to complete but thinks they should be able to complete it in 1,250 hours. If everything goes smoothly, it could take only 1,100 hours.
Answer: A
1,283 hours
Using the triangular distribution method, the expected duration for the project can be calculated by taking the average of the three estimates provided: the minimum (1,100 hours), the most likely (1,250 hours), and the maximum (1,500 hours). Applying the formula for the mean of a triangular distribution results in an expected duration of 1,283 hours.
A) 1,283 hours
This option is correct because it represents the calculated mean of the triangular distribution using the provided estimates. The mean is derived by the formula: (minimum + most likely + maximum) / 3, which gives (1,100 + 1,250 + 1,500) / 3 = 1,283 hours.
B) 1,250 hours
This option is incorrect as it only represents the most likely duration but does not take into account the variability of the other estimates. While this duration is a key component of the triangular distribution, it does not reflect the expected value which is calculated from all three estimates.
C) 1,269 hours
This option is incorrect because it does not align with the triangular distribution calculation. The expected duration must be calculated based on the provided minimum, most likely, and maximum estimates, leading to a mean of 1,283 hours, making 1,269 hours an inaccurate representation.
D) 1,100 hours
This option is incorrect as it represents the minimum duration estimate. While it is the lowest estimate provided, it does not account for the likelihood of the most likely and maximum durations, thus failing to reflect the expected duration of the project.
Conclusion
The correct answer, 1,283 hours, is derived from the proper application of the triangular distribution method, which considers all estimates provided. Other options fail to represent the average duration calculated from the minimum, most likely, and maximum estimates, demonstrating a misunderstanding of the triangular distribution concept.