Question

Consider the following work breakdown structure:What is the probability that this project will be completed within 210 days AND after 195 days? Time Estimates (days) Activity Precedes Optimistic Most Likely Pessimistic Start A,B,C - - - A D 38 50 62 B E 90 99 108 C E 70 80 90 D E,F 19 25 31 E End 91 100 115 F End 62 65 68
a) 0.815.
b) 0.8413.
c) 0.95.
d) 0.9772.

Answer 1

Answer: 0.8186  

Explanation:

Given that;

activity To    Tm Tp     Te (V)^0.5            v

A         38    50 62    50 4                   16

B         90    99 108    99 3                    9

C         70    80 90    80 3.333333    11.11111

D         19    25 31    25 2                    4

E         91    100 115    101 4                   16

F         62    65 68    65 1                    1

Expected duration Te = (4 × Tm + To + Tp ) / 6

Variance = ( Tp-To/6]²

variance of the critical path = 9+16 =25

SD of the critical path = ( var)^0.5 = 5

probability that the project will be completed within  210 days is given by

z = (210-200) / 5 = 2

which gives probability of 0.97725

Probability that the project will be completed within 195 days

z = (195-200) / 5 = -1

which corresponds to probability of 0.1586

Now required probability that project completes within 210 but before 195 days is given by

0.97725 - 0.1586 = 0.8186