Question

Activity	Predecessor	Optimistic Time (a)	Most Probable Time (m)	Pessimistic Time (b)
A	None	2	6	10
B	None	2	4	6
C	A	2	4	6
D	A	4	6	8
E	B	6	8	22
F	B	6	8	10
G	C,D	2	8	12
H	E,F	2	7	12
I	G,H	4	8	16

Question for Blank 1: What is the Critical Path?

Question for Blank 2: What is the Expected Duration of the Project? round to nearest whole number

Question for Blank 3: If a Target of 35 days is given, what is the probability of the project being completed on or before the Target date?

Answer 1

EXPECTED TIME

FORMULA:

(a + (4m) + b) / 6

A = (2 + (4 * 6) + 10) / 6 = 6

B = (2 + (4 * 4) + 6) / 6 = 4

C = (2 + (4 * 4) + 6) / 6 = 4

D = (4 + (4 * 6) + 8) / 6 = 6

E = (6 + (4 * 8) + 22) / 6 = 10

F = (6 + (4 * 8) + 10) / 6 = 8

G = (2 + (4 * 8) + 12) / 6 = 7.67

H = (2 + (4 * 7) + 12) / 6 = 7

I = (4 + (4 * 8) + 16) / 6 = 8.67

VARIANCE

FORMULA:

((b - a) / 6) ^ 2

A = (10 - 2) / 6) ^ 2 = 1.78

B = (6 - 2) / 6) ^ 2 = 0.44

C = (6 - 2) / 6) ^ 2 = 0.44

D = (8 - 4) / 6) ^ 2 = 0.44

E = (22 - 6) / 6) ^ 2 = 7.11

F = (10 - 6) / 6) ^ 2 = 0.44

G = (12 - 2) / 6) ^ 2 = 2.78

H = (12 - 2) / 6) ^ 2 = 2.78

I = (16 - 4) / 6) ^ 2 = 4

CPM ANALYSIS

ACTIVITY	DURATION	ES	EF	LS	LF	SLACK
A	6	0	6	1.33	7.33	1.33
B	4	0	4	0	4	0
C	4	6	10	9.33	13.33	3.33
D	6	6	12	7.33	13.33	1.33
E	10	4	14	4	14	0
F	8	4	12	6	14	2
G	7.67	12	19.67	13.33	21	1.33
H	7	14	21	14	21	0
I	8.67	21	29.67	21	29.67	0

FORWARD PASS = ES = MAX EF OF THE PREDECESSOR

EF = ES + DURATION

BACKWARD PASS = LF = MIN LS OF ALL PREDECESSORS

LS = LF - DURATION

CRITICAL PATH = PATH WITH LONGEST DURATION AND 0 NET SLACK

CRITICAL PATH & DURATION

B + E + H + I = 29.67

WE CAN TAKE THE TIME OF COMPLETION TO BE EITHER 29.67 OR 30, TO ROUND IT UP TO THE NEAREST INTEGER

VARIANCE OF CRITICAL PATH = 0.44 + 7.11 + 2.78 + 4 = 14.33

Due time = 35

Expected time = 30

Stdev = sqrt(variance) = sqrt(14.33) = 3.7855(ROUNDED)

Z = DUE - EXPECTED / STDEV

Z = 35 - 30 / 3.7855 = 1.3208

Z value of 1.3208 gives a distribution of 0.9067 OR 90.67 % probability of completion of the project by the due time of 35

**INTERMEDATECALCULATIONS FOR PROBABILISTIC ESTIMATES ROUNDED TO 4 DECIMAL PLACES.