a) Calculate the expected durations, variance, and standard deviation for each project activity b) Using Table 1 and Table 2, determine the probability of completing the project in 53 weeks. c) Using clearly annotated diagrams show the above project network as (1) Activity on Arrow (ii) Activity on Node

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Table 1 gives the optimistic, most likely, and pessimistic time estimates in weeks for
each activity (represented as event or alphabet as may be appropriate).
ACIVITY
(1-2) (A)
2-3 (B)
2-4 (C)
3-5 (C)
4-5 (D)
5-6(E)
O = optimistic durations in weeks
M = most probable (likely) durations in weeks
P = pessimistic durations in weeks
Z
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
NOTE:
Areas
OPTIMISTIC (0)
0.0
0.040
0.079
0.118
8
6
14
2
6
4
0.155
0.192
0.226
0.258
0.288
0.316
Table 2. Area under one-half the normal distribution for various durations expressed as Z,
where Z= (D-Te)/ST
Z
MOST LIKELY (M)
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Area
0.341
0.364
0.385
0.403
0.419
0.433
0.475
0.455
12
12
20
4
0.464
0.471
12
10
Z
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
PESSIMISTIC
18
16
Area
24
8
c) Using clearly annotated diagrams show the above project network as
(1) Activity on Arrow
(ii) Activity on Node
20
14
0.477
0.482
0.486
0.489
0.492
0.494
0.495
0.496
0.497
0.4998
0.4999
As the curve is symmetrical, the same value occurs for -Z as for +Z. Also note
that the total area under one-half the curve equals 0.5
a) Calculate the expected durations, variance, and standard deviation for each project
activity
b) Using Table 1 and Table 2, determine the probability of completing the project
in 53 weeks.
Transcribed Image Text:Table 1 gives the optimistic, most likely, and pessimistic time estimates in weeks for each activity (represented as event or alphabet as may be appropriate). ACIVITY (1-2) (A) 2-3 (B) 2-4 (C) 3-5 (C) 4-5 (D) 5-6(E) O = optimistic durations in weeks M = most probable (likely) durations in weeks P = pessimistic durations in weeks Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 NOTE: Areas OPTIMISTIC (0) 0.0 0.040 0.079 0.118 8 6 14 2 6 4 0.155 0.192 0.226 0.258 0.288 0.316 Table 2. Area under one-half the normal distribution for various durations expressed as Z, where Z= (D-Te)/ST Z MOST LIKELY (M) 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Area 0.341 0.364 0.385 0.403 0.419 0.433 0.475 0.455 12 12 20 4 0.464 0.471 12 10 Z 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 PESSIMISTIC 18 16 Area 24 8 c) Using clearly annotated diagrams show the above project network as (1) Activity on Arrow (ii) Activity on Node 20 14 0.477 0.482 0.486 0.489 0.492 0.494 0.495 0.496 0.497 0.4998 0.4999 As the curve is symmetrical, the same value occurs for -Z as for +Z. Also note that the total area under one-half the curve equals 0.5 a) Calculate the expected durations, variance, and standard deviation for each project activity b) Using Table 1 and Table 2, determine the probability of completing the project in 53 weeks.
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