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Project management: probability of completing all activities

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I want assistance with c(i) and c(ii) only in following question.

The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the following table:

Activity Immediate predecessor Activity time (weeks)
A - 3
B - 6
C A 2
D B,C 5
E D 4
F E 3
G B,C 9
H F,G 3

a. Draw a network diagram for this problem.
b. Determine the critical path and the expected project completion time.
c. Assume the project variance is 4 weeks.
i. What is the probability that all the activities are completed within 19 weeks?
ii. When is the due date if there is a 90% of completing all the activities?

Here is what I have done so far.

a) To calculate the probability in c(i) question is to put

P(complete) = P (x < 19)
P (z< 21-19/ square root 4)
P (z<2/2)
P (z <1)
0.8413

So it is 84.13%. Is this correct?

b) To calculate expected date of completion in c(ii) is to calculate for each of the possible task which is

90/100 x 20 = 18

So 1 = dd- 18 /2

Then answer is 20. Is this correct?

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As per your message you want assistance with c(i) and c(ii) only, so I will restrict this response to these.

Since we do not have information on optimistic, pessimistic and most likely time estimates for various tasks, we would consider expected time as the time taken on critical path B-D-E-F-H (rather than the sum of all the expected durations on the critical path), that is, 21 weeks.

Expected Duration of project completion = Te = 21 weeks
Project variance ...

Solution Summary

As question is asking for assistance with c(i) and c(ii) only, this solution addresses only these two.
Since the interpretation of "When is the due date if there is a 90% of completing all the activities?" is not clear, this solution considers that it is asking us to compute the due date if there is 90% of completing all the activities in 19 weeks.

$2.19
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13-20
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ACTIVITY DAYS IMMEDIATE
PREDECESSORS
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I 10 11 12 G
J 14 16 20 C
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