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.
[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.
