PERT Analysis MCQ with answer and solution

Concept

Project Duration Range and Standard Deviation

Formula

T_total = Σ T_i, σ_total = √(Σ σ_i²), Range = T_total ± 3σ_total

Step-by-step solution

1. Calculate mean duration: T\_total = T + T + T + T = 4T 2. Calculate total variance: σ\_total² = k² + k² + k² + k² = 4k² 3. Calculate standard deviation: σ\_total = √(4k²) = 2k 4. Apply 3σ range: Range = 4T ± 3(2k) = 4T ± 6k

Explanation

For four consecutive activities, the total mean project duration is the sum of their individual mean durations: T + T + T + T = 4T. To find the overall standard deviation, we first calculate the total variance by adding the variances of each activity: k² + k² + k² + k² = 4k². The overall standard deviation is the square root of the total variance, which is √(4k²) = 2k. In statistics, project duration generally falls within three standard deviations (3σ rule) from the mean (99.73% confidence level). Multiplying 3 by the overall standard deviation of 2k gives 6k. Therefore, the overall project duration is likely to fall in the range of 4T ± 6k.

Shortcut

Total SD = √(number of activities) × k = √4 × k = 2k. Apply the 3-σ rule: range = Mean ± 3 × (Total SD) = 4T ± 3(2k) = 4T ± 6k.

Common mistake

A common mistake is directly adding the standard deviations (k + k + k + k = 4k) instead of summing the variances (k² + k² + k² + k² = 4k², giving an overall standard deviation of 2k), leading students to incorrectly choose Option C (4T ± 4k) or Option B (4T ± 2k) by forgetting to apply the 3-σ rule (3 × 2k = 6k).