Question

M5_A2. The Mountaineers American Bank of Carolina is planning to install a new computerized accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and the activity time estimates, as shown in the table below.

activity	optim time (a)	most likely time (m)	pessim time (b)	immediate Pred
A	5	8	17	---
B	3	12	15	---
C	4	7	10	A
D	5	8	23	A
E	1	1	1	B,C
F	1	4	13	B,C
G	3	6	9	D,E
H	1	2.5	7	D,E
I	1	1	1	H
J	2	2	2	F,G
K	5	8	11	I,J

Calculate the expected duration and variances for each activity. Use the expected durations to develop a project network for this problem and answer the following questions (Note: when using the Z tables –round your Z values to two decimal places before getting the probabilities from the tables. DO NOT round standard deviations prior to calculating Z values)

NOTE: Enter probabilities as decimals (i.e 92.31% should be entered as 0.9231)

a) What activities are on the critical path? (Select all activities that are on critical path)

b) How many days will it take to complete the project?

c) What is the total variance of the project (i.e. the activities that are on the critical path)? (Enter

to two decimal places)

d) What is the total standard deviation of the project (i.e. the activities that are on the critical

path)? (Enter standard deviation to three decimal places)

e) What is the probability that the project will be completed in less than 34 weeks to complete?

(Enter probability to four decimal places from distribution tables)

f) What is the probability that the project will take more than 29 weeks to complete? (Enter

probability to four decimal places from distribution tables)

g) What is the probability that the project will between 30 and 38 weeks to complete? (Enter

probability to four decimal places from distribution tables)

Answer 1

Activity	a	m	b	estimated time(ei)	SD	Variance
A	5	8	17	9	2	4
B	3	12	15	11	2	4
C	4	7	10	7	1	1
D	5	8	23	10	3	9
E	1	1	1	1	0	0
F	1	4	13	5	2	4
G	3	6	9	6	1	1
H	1	2.5	7	3	1	1
I	1	1	1	1	0	0
J	2	2	2	2	0	0
K	5	8	11	8	1	1

From the given data we have below table

Different possible paths areBelow is the PERT diagram

Paths	Duration
ADHIK	31
ADGJK	35
ACEHIK	29
ACEGJK	33
ACFJK	31
BEHIK	24
BEGJK	28
BFJK	26

Hence critical path is ADGJK with duration 35 days

(A) Activities on critical path are A, D, G, J and K

(B) It will take 35 days to complete the project

(C) Total variance of the project = sum of variance of the activities on critical path = 15 days

(D) std. dev. = sqrt(15) = 3.873 days

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