College

Consider the following work breakdown structure:

[tex]
\[
\begin{array}{ccccc}
& & \multicolumn{4}{c}{\text{Time Estimates (days)}} \\
\text{Activity} & \text{Predecessors} & \text{Optimistic} & \text{Most Likely} & \text{Pessimistic} \\
\hline
\text{Start} & A, B, C & 0 & 0 & 0 \\
A & D & 38 & 50 & 62 \\
B & E & 90 & 99 & 108 \\
C & \text{End} & 85 & 100 & 115 \\
D & F & 19 & 25 & 31 \\
E & \text{End} & 91 & 100 & 115 \\
F & \text{End} & 62 & 65 & 68 \\
\end{array}
\]
[/tex]

What is the estimated expected (mean) time for activity E?

A. 115 days
B. 100 days
C. 91 days
D. 99 days
E. 101 days

Answer :

To find the estimated expected (mean) time for activity E, we use a common formula in project management called the PERT (Program Evaluation and Review Technique) formula to calculate the expected time for an activity. The PERT formula is:

[tex]\[ \text{Expected time} = \frac{\text{Optimistic time} + 4 \times \text{Most likely time} + \text{Pessimistic time}}{6} \][/tex]

Here’s how we calculate it step-by-step:

1. Identify the time estimates for activity E:
- Optimistic time (O) = 91 days
- Most likely time (M) = 100 days
- Pessimistic time (P) = 115 days

2. Apply these values to the PERT formula:
[tex]\[
\text{Expected time} = \frac{91 + 4 \times 100 + 115}{6}
\][/tex]

3. Calculate each part of the formula:
- Multiply the most likely time by 4:
[tex]\[
4 \times 100 = 400
\][/tex]
- Add the optimistic, modified most likely, and pessimistic times:
[tex]\[
91 + 400 + 115 = 606
\][/tex]

4. Divide the total by 6 to find the mean:
[tex]\[
\frac{606}{6} = 101
\][/tex]

Thus, the estimated expected (mean) time for activity E is 101 days.