Question

The following table shows estimates of activity times (weeks) for a project:

Activity	Optimistic Time	Most Probable Time	Pessimistic Time
A	3	4.5	9
B	1.5	2	2.5
C	5	6	7
D	4	4.5	8
E	5	6	7
F	1	2.5	7
G	7	9	11

Suppose that the critical path is A-B-D-F-G. Use Appendix A to answer the questions. Do not round intermediate calculations. Round your answers to three decimal places.

1. What is the probability that the project will be completed within 25 weeks?

Answer 1

Answer: the probability that the project will be completed within 25 weeks is 0.7208 or 72.08%

Explanation:

Activity	Optimistic time-a	Expected completion time-m	Pessimistic time-b	Expected time= (a+4*m+ b)/6	Variance, (sigma)^2= (b-a/6)^2
A	3	4.5	9	5.00	1.00
B	1.5	2	2.5	2.00	0.03
C	5	6	7	6.00	0.11
D	4	4.5	8	5.00	0.44
E	5	6	7	6.00	0.11
F	1	2.5	7	3.00	1.00
G	7	9	11	9.00	0.44

The duration of critical path ABDFG is 24 weeks,

step 1	we will find the variance of the tasks which lie on critical path				2.92
step 2	mean project time (u) of critical path is=				24.00
step 3	Required completion time is				25
step 4	standard deviation= sqrt(variance)=				1.709
step 5	because Z= (given completion time- u)/standard deviation				0.585
step 6	P(z)= using NORM.S.DIST(z,true)				0.7208

the probability that the project will be completed within 25 weeks is 0.7208

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