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2. A project has the following activities, precedence relationships, and time estimates in weeks: Activity | Immediate Predecessor Activities | Optimistic Time (a) | Most Likely Time (m) | Pessimistic Time (b) --- | --- | --- | --- | --- A | — | 15 | 20 | 25 B | — | 8 | 10 | 12 C | A | 25 | 30 | 40 D | B | 15 | 15 | 15 E | B | 22 | 25 | 27 F | E | 15 | 20 | 22 G | D | 20 | 20 | 22 a. Compute the expected time and variance for each activity. b. Determine the critical path and the expected duration of the project. c. What is the probability that the project will take longer than 56 weeks to complete? d. What is the probability that the project will be completed in less than 54 weeks?

          2. A project has the following activities, precedence relationships, and time estimates in weeks:

Activity | Immediate Predecessor Activities | Optimistic Time (a) | Most Likely Time (m) | Pessimistic Time (b)
--- | --- | --- | --- | ---
A | — | 15 | 20 | 25
B | — | 8 | 10 | 12
C | A | 25 | 30 | 40
D | B | 15 | 15 | 15
E | B | 22 | 25 | 27
F | E | 15 | 20 | 22
G | D | 20 | 20 | 22

a. Compute the expected time and variance for each activity.
b. Determine the critical path and the expected duration of the project.
c. What is the probability that the project will take longer than 56 weeks to complete?
d. What is the probability that the project will be completed in less than 54 weeks?

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2. A project has the following activities, precedence relationships, and time estimates in weeks:

Activity | Immediate Predecessor Activities | Optimistic Time (a) | Most Likely Time (m) | Pessimistic Time (b)
— | — | — | — | —
A | — | 15 | 20 | 25
B | — | 8 | 10 | 12
C | A | 25 | 30 | 40
D | B | 15 | 15 | 15
E | B | 22 | 25 | 27
F | E | 15 | 20 | 22
G | D | 20 | 20 | 22

a. Compute the expected time and variance for each activity.
b. Determine the critical path and the expected duration of the project.
c. What is the probability that the project will take longer than 56 weeks to complete?
d. What is the probability that the project will be completed in less than 54 weeks?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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2. A project has the following activities, precedence relationships, and time estimates in weeks: Activity | Immediate Predecessor Activities | Optimistic Time (a) | Most Likely Time (m) | Pessimistic Time (b) --- | --- | --- | --- | --- A | — | 15 | 20 | 25 B | — | 8 | 10 | 12 C | A | 25 | 30 | 40 D | B | 15 | 15 | 15 E | B | 22 | 25 | 27 F | E | 15 | 20 | 22 G | D | 20 | 20 | 22 a. Compute the expected time and variance for each activity. b. Determine the critical path and the expected duration of the project. c. What is the probability that the project will take longer than 56 weeks to complete? d. What is the probability that the project will be completed in less than 54 weeks?

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Transcript

00:01 Hello students, according to the given question by observing we can say that expected time will be equal to optimistic time plus 4 into most likely time plus pessimistic time is divided by 6.

00:50 Now variance will be equal to pessimistic time minus optimistic time is divided by 6 whole square.

01:23 Now here there is an activity and here there is an expected time and here it is variance.

01:41 Now for the activity a expected time will be 15 plus 4 into 19 plus 25 is divided by 6 which is equal to 19 .33 and variance will be 25 minus 15 is divided by 6.

02:13 Which is equal to 2 .7778.

02:18 In the activity b, expected time will be 8 plus 4 into 11 plus 12 is divided by 6 which is equal to 10 .67.

02:35 And the variance will be 12 minus 8 is divided by 6.

02:42 4 square which is equal to 0 .4444.

02:49 Now for the activity c, expected time will be 25 plus 4 into 29 plus 40 is divided by 6 which is equal to 30 .17 and the variance will be 40 minus 40.

03:14 25 is divided by 6 whole square which is equal to 6 .25.

03:25 For the activity d, expected time will be 15 plus 4 into 15 plus 15 is divided by 6 which is equal to 15.

03:41 And the variance will be 15 minus 15 is divided by 6 whole square which is equal to 0 and for the activity e the expected time will be 22 plus 4 into 24 plus 27 is divided by 6 which is equal to 24 .1 is divided by 6 which is equal to 24 .1 and the variance is 27 minus 22 is divided by 6 whole square which is equal to 0 .6644...

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