To determine the variance for activity [tex]\(C\)[/tex], we can use the formula for variance in the Program Evaluation and Review Technique (PERT), which is given by:
[tex]\[ \text{Variance} = \left(\frac{b - a}{6}\right)^2 \][/tex]
where:
- [tex]\(a\)[/tex] is the optimistic time estimate,
- [tex]\(m\)[/tex] is the most likely time estimate,
- [tex]\(b\)[/tex] is the pessimistic time estimate.
Given the times for activity [tex]\(C\)[/tex]:
- [tex]\(a = 9\)[/tex] weeks,
- [tex]\(m = 14\)[/tex] weeks,
- [tex]\(b = 18\)[/tex] weeks,
we can substitute these values into the variance formula.
First, calculate [tex]\( \frac{b - a}{6} \)[/tex]:
[tex]\[
\frac{18 - 9}{6} = \frac{9}{6} = 1.5
\][/tex]
Next, square the result to find the variance:
[tex]\[
(1.5)^2 = 2.25
\][/tex]
Therefore, the variance for activity [tex]\(C\)[/tex] is [tex]\(2.25\)[/tex] weeks.
