In Project Management, when we are given a range of possible durations, we use the Three-Point Estimating formula to determine the expected duration ($t_E$).

While there are two formulas, the standard calculation for this problem (Triangular Distribution) is:

$$t_E = \frac{O + M + P}{3}$$

Where:

$O$ (Optimistic): 2 days

$M$ (Most Likely): 3 days

$P$ (Pessimistic): 7 days

Calculation:

$$t_E = \frac{2 + 3 + 7}{3}$$

$$t_E = \frac{12}{3}$$

$$t_E = 4$$

Why this matters:

Reduces Bias: Relying on a single " Most Likely " estimate can be risky. Three-point estimating forces the team to consider risks (Pessimistic) and opportunities (Optimistic).

Accuracy: It provides a more mathematically sound average than a simple guess, helping the Project Manager create a more realistic Schedule Baseline.

Note on PERT (Beta Distribution):

If the question specifically asked for PERT or a Weighted Average, the formula would be $t_E = \frac{O + 4M + P}{6}$. Using PERT for these numbers would result in $3.5$ days. Since $4$ is the available choice that aligns with the simple triangular average, Option C is the correct answer.

Per PMI standards, this technique is used within the Estimate Activity Durations process to improve the accuracy of time estimates when there is uncertainty associated with the activity.