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Mobile App Chapter 1: Q9OQ (page 102)
There is an 82 percent chance the project below can be completed in X weeks or less. What is X?
Short Answer
Expert verified
The value of X is 18 weeks.
Step by step solution
01
The network diagram
The network diagram for the given table is:
02
The expected time
| Activity | Most Optimistic | Most Likely | Most Pessimistic | Expected time |
| A | 2 | 5 | 11 | =(B2+4*C2+D2)/6 |
| B | 3 | 3 | 3 | =(B3+4*C3+D3)/6 |
| C | 1 | 3 | 5 | =(B4+4*C4+D4)/6 |
| D | 6 | 8 | 10 | =(B5+4*C5+D5)/6 |
Activity | Most Optimistic | Most Likely | Most Pessimistic | Expected time |
| A | 2 | 5 | 11 | 5.5 |
| B | 3 | 3 | 3 | 3 |
| C | 1 | 3 | 5 | 3 |
| D | 6 | 8 | 10 | 8 |
| E | 4 | 7 | 10 | 7 |
Now, we can find the expected path durationas follow:
The longest time of 16.5 weeks belongs to the path A-B-D and this path would be the critical pathof the project.
03
The value of X
We know that, to find the variance we can use
| Activity | Most Optimistic | Most Likely | Most Pessimistic | Variance |
| A | 2 | 5 | 11 | =((D2-B2)/6)^2 |
| B | 3 | 3 | 3 | =((D3-B3)/6)^2 |
| C | 1 | 3 | 5 | =((D4-B4)/6)^2 |
| D | 6 | 8 | 10 | =((D5-B5)/6)^2 |
| Activity | Most Optimistic | Most Likely | Most Pessimistic | Variance |
| A | 2 | 5 | 11 | 2.25 |
| B | 3 | 3 | 3 | 0 |
| C | 1 | 3 | 5 | 0.44444444 |
| D | 6 | 8 | 10 | 0.44444444 |
| E | 4 | 7 | 10 | 1 |
Value of 82% using NORMSINV function in excel:
| =NORMSINV(0.82) |
| 0.915365 |
We know that Expected time = X
Scheduled time = 16.5
Standard deviation = 2.69
Probability distribution = 0.915
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