Question

Problem 17-7 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. Use Table B. TIME IN DAYS Immediate Activity Predecessor Optimistic Most Likely Pessimistic 15 12 7 End E,G,1 b.What is the probability that the project can be completed in 24 days or less? In 21 days or less? (Round your te and z values to 2 decimal places and "Standard deviation" to 3 decimal places. Round your final answers to 4 decimal places.) Probability Days 24 days or less 21 days or less

Answer 1

Activity	a	m	b	te = (a +4m +b) / 6	SD = (b - a) / 6	Var = SD2
A	5	6	7	6.00	0.333	0.111
B	8	8	11	8.50	0.500	0.250
C	6	8	11	8.17	0.833	0.694
D	9	12	15	12.00	1.000	1.000
E	5	6	9	6.33	0.667	0.444
F	5	6	7	6.00	0.333	0.111
G	2	3	7	3.50	0.833	0.694
H	4	4	5	4.17	0.167	0.028
I	5	7	8	6.83	0.500	0.250

(b)

There are three different independent paths: A-C-E, B-H-I, and D-F-G

Find the path-wise t_e and variances as shown below

Activity	te	Var
A	6.00	0.111
C	8.17	0.694
E	6.33	0.444
Total	20.50	1.25
	SD	1.118

Activity	te	Var
B	8.50	0.25
H	4.17	0.03
I	6.83	0.25
Total	19.50	0.53
	SD	0.726

Activity	te	Var
D	12.00	1.00
F	6.00	0.11
G	3.50	0.69
Total	21.50	1.81
	SD	1.344

For completion within 24 days

• Path A-C-E: z = (24 - 20.50) / 1.118 = 3.13, So, Prob (Completion) = 0.9991
• Path B-H-I: z = (24 - 19.50) / 0.726 = 6.20, So, Prob (Completion) = 1
• Path D-F-G: z = (24 - 21.50) / 1.344 = 1.86, So, Prob (Completion) = 0.9686

So, Prob(Completion within 24 days) = 0.9991 * 1 * 0.9686 = 0.9677

For completion within 21 days

• Path A-C-E: z = (21 - 20.50) / 1.118 = 0.45, So, Prob (Completion) = 0.6736
• Path B-H-I: z = (21 - 19.50) / 0.726 = 2.07, So, Prob (Completion) = 0.9808
• Path D-F-G: z = (21 - 21.50) / 1.344 = -0.37, So, Prob (Completion) = 0.3557

So, Prob(Completion within 24 days) = 0.6736 * 0.9808 * 0.3557 = 0.2350

(c)

Activity	a	m	b	te = (a +4m +b) / 6	SD = (b - a) / 6
D	5	6	7	6	0.333333333

Activity	te	Var
A	0.00	0.000
C	8.17	0.694
E	6.33	0.444
Total	14.50	1.14
	SD	1.067

Activity	te	Var
B	0.00	0.00
H	4.17	0.03
I	6.83	0.25
Total	11.00	0.28
	SD	0.527

Activity	te	Var
D	6.00	0.333
F	6.00	0.11
G	3.50	0.69
Total	15.50	1.14
	SD	1.067

For completion within 24 days (i.e. in another 17 days)

• Path A-C-E: z = (17 - 14.50) / 1.067 = 2.34, So, Prob (Completion) = 0.9904
• Path B-H-I: z = (17 - 11.00) / 0.527 = 11.39, So, Prob (Completion) = 1
• Path D-F-G: z = (17 - 15.50) / 1.067 = 1.41, So, Prob (Completion) = 0.9207

So, Prob(Completion within 24 days) = 0.9904 * 1 * 0.9207 = 0.9119

For completion within 21 days (i.e. in another 14 days)

• Path A-C-E: z = (14 - 14.50) / 1.067 = -0.47, So, Prob (Completion) = 0.3192
• Path B-H-I: z = (14 - 11.00) / 0.527 = 5.69, So, Prob (Completion) = 1
• Path D-F-G: z = (14 - 15.50) / 1.067 = -1.41, So, Prob (Completion) = 0.0793

So, Prob(Completion within 24 days) = 0.3192 * 1 * 0.0793 = 0.0253