The optimistic, most likely and pessimistic time estimates of an activity are 6, 12 and 22 days respectively. What is the standard deviation?
- A1
- B1.67
- C2.67Correct
- D7.12
Solution
Concept
Standard deviation calculation in PERT analysis
Formula
(tp - to) / 6
Step-by-step solution
1. Optimistic time = 6 days, pessimistic time = 22 days. 2. Standard deviation = (22 - 6) / 6 = 16 / 6 = 2.67 days. Answer: C
Explanation
In PERT analysis, standard deviation is calculated as one-sixth of the difference between pessimistic time and optimistic time. Subtracting 6 from 22 gives 16, and dividing 16 by 6 yields approximately 2.67. Therefore, option C is the correct answer.
Why the other options are wrong
A) 1 does not equal the calculated standard deviation of time estimates. D) 7.12 is significantly higher than the standard deviation value.
Shortcut
Standard Deviation (SD) = (Pessimistic - Optimistic) / 6 = (22 - 6) / 6 = 2.67.
Common mistake
Calculating expected time (O + 4M + P)/6 instead of standard deviation (P - O)/6.
Correct answer: C) 2.67