For a given activity, the optimistic time, pessimistic time and the most probable estimates are 5, 8 and 17 days respectively.
- A8 days
- B9 daysCorrect
- C10 days
- D15 days
Solution
Concept
PERT Expected Time
Formula
TE = (To + 4Tm + Tp) / 6
Step-by-step solution
1. Identify the given values: Optimistic time (To) = 5, Most probable time (Tm) = 8, Pessimistic time (Tp) = 17. 2. Apply the PERT formula: TE = (To + 4 × Tm + Tp) / 6 3. Substitute the values: TE = (5 + 4 × 8 + 17) / 6 4. Simplify the numerator: TE = (5 + 32 + 17) / 6 = 54 / 6 5. Calculate the result: TE = 9 days
Explanation
To find the expected time in PERT, use the formula: (Optimistic + 4 × Most Probable + Pessimistic) ÷ 6. Plugging in the given values: (5 + 4 × 8 + 17) ÷ 6 = (5 + 32 + 17) ÷ 6 = 54 ÷ 6 = 9 days. Therefore, option B (9 days) is correct.
Shortcut
Focus on the 1-4-1 weighted ratio: multiply the middle (most probable) value by 4, add the lowest (optimistic) and highest (pessimistic) values, then divide the total sum by 6. Ignore any additional table data provided in the question.
Common mistake
A common mistake is simply averaging the three time estimates (To + Tm + Tp) / 3 = (5 + 8 + 17) / 3 = 10 days (Option C), forgetting to apply the weighted PERT formula where the most probable time is multiplied by 4, or getting distracted by the irrelevant resource table data included in the question.
Correct answer: B) 9 days