To determine the expected (estimated) time for activity [tex]\( C \)[/tex], we use the Program Evaluation and Review Technique (PERT) formula:
[tex]\[ \text{Expected time} = \frac{a + 4m + b}{6} \][/tex]
where:
- [tex]\( a \)[/tex] is the optimistic time
- [tex]\( m \)[/tex] is the most likely time
- [tex]\( b \)[/tex] is the pessimistic time
For activity [tex]\( C \)[/tex]:
- [tex]\( a = 9 \)[/tex]
- [tex]\( m = 14 \)[/tex]
- [tex]\( b = 18 \)[/tex]
Substitute these values into the PERT formula:
[tex]\[ \text{Expected time} = \frac{9 + 4(14) + 18}{6} \][/tex]
Calculate step-by-step:
1. First, calculate the weighted sum of the times:
[tex]\[ 9 + 4(14) + 18 = 9 + 56 + 18 \][/tex]
2. Sum these values:
[tex]\[ 9 + 56 + 18 = 83 \][/tex]
3. Divide the sum by 6:
[tex]\[ \frac{83}{6} \approx 13.83 \][/tex]
Therefore, the expected (estimated) time for activity [tex]\( C \)[/tex] is [tex]\(\boxed{13.83}\)[/tex] weeks.
