Question

In a PERT network for an activity Pessimistic, Most likely, and Optimistic times are 8 days, 6 days and 4 days respectively. The expected duration of the activity is _______

• A. 6 days
• B. 2 days
• C. 8 days
• D. 9 days

Hint:

Notice that the "most likely" time is given the most weight (a factor of 4) in the PERT formula.
This pulls the expected time towards the most probable outcome.
In this case, since the time estimates are symmetric around the most likely time (6-2=4, 6+2=8), the expected time is equal to the most likely time.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We need to calculate the "expected duration" of a single activity using the PERT (Program Evaluation and Review Technique) three-point estimate.

Step 2: Key Formula or Approach:
The PERT formula for the expected time (\(t_e\)) of an activity is a weighted average of the three estimates:
\[ t_e = \frac{t_o + 4t_m + t_p}{6} \] where: - \(t_o\) = Optimistic time (best-case scenario) - \(t_m\) = Most likely time - \(t_p\) = Pessimistic time (worst-case scenario)

Step 3: Detailed Explanation:
From the question, we have: - Optimistic time, \(t_o = 4\) days - Most likely time, \(t_m = 6\) days - Pessimistic time, \(t_p = 8\) days
Substitute these values into the formula:
\[ t_e = \frac{4 + (4 \times 6) + 8}{6} \] \[ t_e = \frac{4 + 24 + 8}{6} \] \[ t_e = \frac{36}{6} = 6 \, \text{days} \]

Step 4: Final Answer:
The expected duration of the activity is 6 days.
This corresponds to option (A).