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PMP Practice: Assess Plans for Dependencies and Gaps

Question 15 of 15 in Develop an Integrated Project Management Plan

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Chidera Nwosu is managing a warehouse automation project for Ambitious Napkin Inc. The project includes installing robotic sorting systems across four phases. During planning, the team provides the following effort estimates for Phase 2 (conveyor belt integration): Optimistic estimate: 18 days Most likely estimate: 24 days Pessimistic estimate: 42 days Lila needs to calculate a weighted average duration for this phase to support resource planning. The project sponsor has requested that Lila also calculate the standard deviation to understand the variability risk, as Phase 2 is on the critical path and any delay will impact the warehouse opening date. Using the three-point estimation technique, what is the expected duration for Phase 2, and what is the standard deviation?
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Correct answer: Expected duration: 26 days; Standard deviation: 4 days

Explanation

Using the three-point estimation formula, the expected duration is calculated as (Optimistic + 4×Most Likely + Pessimistic) ÷ 6. Substituting the values: (18 + 4×24 + 42) ÷ 6 = (18 + 96 + 42) ÷ 6 = 156 ÷ 6 = 26 days. The standard deviation represents the variability and is calculated as (Pessimistic − Optimistic) ÷ 6 = (42 − 18) ÷ 6 = 24 ÷ 6 = 4 days. This weighted average approach gives more emphasis to the most likely estimate, which reflects the team's best judgment based on their experience. The standard deviation of 4 days helps Lila communicate the uncertainty range to the sponsor and supports informed decision-making about schedule buffers for this critical path activity.

**Why not A:** An expected duration of 26 days with a standard deviation of 8 days is incorrect because the standard deviation formula is (Pessimistic - Optimistic) ÷ 6, which yields (42 - 18) ÷ 6 = 4 days, not 8 days. Using 8 suggests dividing the range by 3 instead of 6, which is an incorrect application of the formula.

**Why not B:** An expected duration of 24 days with a standard deviation of 4 days uses the correct standard deviation but incorrectly calculates the expected duration. Using 24 days means simply taking the most likely estimate without applying the PERT weighted average formula. The three-point formula accounts for optimistic and pessimistic scenarios, yielding 26 days.

**Why not D:** An expected duration of 28 days with a standard deviation of 6 days is incorrect on both counts. The expected duration of 28 does not result from the PERT formula (18 + 96 + 42) ÷ 6 = 26, and the standard deviation of 6 does not result from (42 - 18) ÷ 6 = 4.

Key Concept

This question covers Assess Plans for Dependencies and Gaps under Develop an Integrated Project Management Plan (Process).

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