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Question 1 (50 points). You were recently assigned to manage a project for your company. You have constructed a network diagram (depicting the various activities in the project, see figure below). In addition, you have asked your team to estimate the amount of time (in days) that they would expect each of the activities to take. Their responses are shown in the table below: Start Finish Table 1 - Estimates Data Time Estimates (Days) Activity OptimisticMost Likely Pessimistic 4 14 4 12 4 a. What is the expected time and variance for each activity? b. What is the expected completion time of the project? c. What is the probability of completing the project in 21 days? d. What is the probability of completing the project in 18 days?

Answer 1

Te = (To+4*Tp+Tm)/6

Variance = [( Tm-To)/6]²

Activity	To	Tm	Tp	Te	Sigma	Sigma^2
A	5	8	11	8	1	1
B	4	9	14	9	1.666667	2.777778
C	5	7	9	7	0.666667	0.444444
D	2	4	12	5	1.666667	2.777778
E	4	7	10	7	1	1

The critical path is ADE with expected project duration of 20 days

SD of critical path = ( 1+ 2.777+1)^1/2 =2.185

Probability of completing the project in 21 days

z = x ( days in case) - mu ( avg completion time) / SD of critical path

z = 21-20 /2.185 = 0.4576

which corresponds to probability of 0.675

Probability of completing the project in 18 days

z = 18-20/2.185 = -0.9153

which corresponds to probability of 0.1814.