Question

Problem 5-11 There is an 82 percent chance the project below can be completed in X weeks or less. B E MOST OPTIMISTIC 2 MOST LIKELY PESSIMISTIC MOST ACTIVITY A 5 11 3 3 3 C 1 5 10 10 4 7 What is X? (Do not round intermediate calculations. Round your answer to the nearest whole number.) X LO CON

Answer 1

Activity	Most Optimistic	Most Likely	Most pessimistic	Expected completion time	Variance
A	2	5	11	5.5	2.25
B	3	3	3	3	0
C	1	3	5	3	0.444444
D	6	8	10	8	0.444444
E	4	7	10	7	1

Expected completion time = (Most optimistic+ Most pessimistic+4*Most Likely)/6

Variance = ((Most pessimistic - Most optimistic)/6)^2

Path	Duration
A-B-D	16.5
A-C-E	15.5

Critical path = A-B-D with duration 16.5 weeks which is project duration and project variance = variance of critical path A-B-D =  2.694444444

Project standard deviation = sqrt(2.694444444) = 1.6414763

z-score for 0.82 probability is 0.92

So, 0.92 = (x-16.5)/1.6414763

or, x = 0.92*1.6414763 + 16.5 = 18.0101582 = 18 (Rounded to nearest whole number)