Question

The following table contains information related to the major activities of a research project. Use the information to do the following:

a. Compute the expected duration, variance, and standard deviation for each activity

b. What is the probability that the project finishes in less than 60 days?

Activity	Predecessor	To	Tm	Tp
A	-	3	7	12
B	A	8	11	17
C	B	7	13	16
D	B	7	10	13
E	C	14	17	23
F	D	12	16	19
G	E, F	5	7	9

Answer 1

Expected time = (To + 4*Tm + Tp)/6

Variance = (Tp-To)^2/36

Standard deviation = sqrt(Variance)

Activity	To	Tm	Tp	Expected Time	Variance	Standard deviation
A	3	7	12	7.17	2.25	1.50
B	8	11	17	11.50	2.25	1.50
C	7	13	16	12.50	2.25	1.50
D	7	10	13	10.00	1.00	1.00
E	14	17	23	17.50	2.25	1.50
F	12	16	19	15.83	1.36	1.17
G	5	7	9	7.00	0.44	0.67

Probability to complete in less than 60 days will be product of probability of two path to complete the project in 60 days

z value = (Estimated time - Expected time)/Standard deviation

Estimated time = 60

z value for path ABCEG = (60 - 55.67)/3.07 = 1.41

Probability for z value 1.41 is 0.9207

z value for path ABDFG = (60 - 51.50)/2.70 = 3.14

Probability for z value 3.14 is 0.9992

Probability for project = 0.9207*0.9992 = 0.9200