Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table

Activity | Immediate Predecessor | Optimistic | Most Likely Pessimistic
A — 5 6 7
B — 8 8 11
C A 6 8 11
D — 9 12 15
E C 5 6 9
F D 5 6 7
G F 2 3 7
H B 4 4 5
I H 5 7 8
End E, G, I
b. Suppose it is now the end of the seventh day and that activities A and B have been completed while activity D is 50 percent completed. Time estimates for the completion of activity D are 5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing the project by day 24 and the probability of finishing by day 21. (Round your intermediate calculations to 3 decimal places and final answers to 4 decimal places.)

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azikennamdi azikennamdi · Answer 1 · 2022-05-11T13:10:37+02:00

The precedence diagram for the problem above is attached. See the definition of a precedence diagram and the probability calculations below.

A precedence diagram is an optical or graphical representation tool that displays a project's activities.

Recall that:

z = (Specified Time - Path's mean)/Path's Standard Deviation.

Hence for z₂₁

(21 − 20.5)/1.118 = 0.447 ≈ 0.45.

Hence the probability is: P(Z<0.45) =0.6736

(21 − 21.5)/1.344 = −0.3721 ≈ −0.37

Hence the probability is: P(Z<-.37) = 0.3557

(21 − 19.5)/.726 = 2.066 ≈ 2.07

Hence the probability is: P(Z<2.07) = 0.9808

Following through on the above, the project will be finished in less than 21 days is given as:

P = 0.23499920921

P ≈ 0.2350

Learn more about Probability at:

https://brainly.com/question/24756209

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