Question

Given the project information in the following table, what is the probability of completing the National Holiday Toy project in 98-time units? Hint: Use the =NORM.S.DISTIZ, TRUE) function in Excel to compute the probability (Carry at least 3 decimal places in all intermediate calculations and the Z value. Enter your final probability answer to 3 decimal places.) (b) Acet. ID 1 2 3 4 5 6 7 Description Design package Design product Build package Secure patent Build product Paint Test market Optimistic Most LikelyPessimistic activity Variance Predecessor (a) Time (te) [(b - a)/612 Critical ? None 6 12 24 13 1 16 19 28 20 4 1 4 7 10 7 1 2 21 30 39 30 9 2 17 29 47 30 25 x 3,4,5 4 7 12 7.33 1.78 6 13 15 19 15.33 1 The probability of completing the project in 9 time units is

Answer 1

Activity Time=(Optimistic+(4*Most Likely)+Pessimistic)/6

Variance=((Pessimistic-Optimistic)/6)^2

1	B	C	D	E	F	G	H	I
2	Activity ID	Predecessor	Optimistic	Most Likely	Pessimistic	Activity Time=(Optimistic+(4*Most Likely)+Pessimistic)/6	Variance=((Pessimistic-Optimistic)/6)^2	Critical activities
3	1	---	6	12	24	13	9.00	Yes
4	2	1	16	19	28	20	4.00	Yes
5	3	1	4	7	10	7	1.00
6	4	2	21	30	39	30	9.00	Yes
7	5	2	17	29	47	30	25.00	Yes
8	6	3,4,5	4	7	12	7	1.78	Yes
9	7	6	13	15	19	15	1.00	Yes
10					Project completion time	85
11					Variance of critical path 1	16.778
12					Variance of critical path 2	40.778
13					Standard Deviation of critical path 1	4.096
14					Standard Deviation of critical path 2	6.386

1	B	C	D	E	F	G	H	I
2	Activity ID	Predecessor	Optimistic	Most Likely	Pessimistic	Activity Time=(Optimistic+(4*Most Likely)+Pessimistic)/6	Variance=((Pessimistic-Optimistic)/6)^2	Critical activities
3	1	---	6	12	24	=(D3+(4*E3)+F3)/6	=((F3-D3)/6)^2	Yes
4	2	1	16	19	28	=(D4+(4*E4)+F4)/6	=((F4-D4)/6)^2	Yes
5	3	1	4	7	10	=(D5+(4*E5)+F5)/6	=((F5-D5)/6)^2
6	4	2	21	30	39	=(D6+(4*E6)+F6)/6	=((F6-D6)/6)^2	Yes
7	5	2	17	29	47	=(D7+(4*E7)+F7)/6	=((F7-D7)/6)^2	Yes
8	6	3,4,5	4	7	12	=(D8+(4*E8)+F8)/6	=((F8-D8)/6)^2	Yes
9	7	6	13	15	19	=(D9+(4*E9)+F9)/6	=((F9-D9)/6)^2	Yes
10					Project completion time	85
11					Variance of critical path 1	=H3+H4+H5+H8+H9
12					Variance of critical path 2	=H3+H4+H7+H8+H9
13					Standard Deviation of critical path 1	=SQRT(G11)
14					Standard Deviation of critical path 2	=SQRT(G12)

Network Diagram:

13 | 2 133 이 20 | 0 13 33. 33 |4 | 63 0 30 | 0 33 63 0 0 0 1 13 13 | 01 13 63 6170 0 17 이 63 70 13 43 56. 3 | 20 7143 63. 33 0 33 5 63 30 | 0 63 70 0 70 17 85 15 | 01 85

Critical path 1: 1-2-4-6-7

Given, X =98

Thus, Value of Z score = (X- μ)/ Standard Deviation = (98-85)/4.096 = 3.17 (Rounded up to 2 Decimal Numbers)

Thus, using Z table, the probability that the project will complete within 98 =99.92%

Critical path 1: 1-2-5-6-7

Given, X =98

Thus, Value of Z score = (X- μ)/ Standard Deviation = (98-85)/6.386 = 2.04 (Rounded up to 2 Decimal Numbers)

Thus, using Z table, the probability that the project will complete within 98 =97.93%