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.

0.8186  

Explanation:

Given that;

activityTo    TmTp     Te(V)^0.5            v

A         38    5062    504                   16

B         90    99108    993                    9

C         70    8090    803.333333    11.11111

D         19    2531    252                    4

E         91    100115    1014                   16

F         62    6568    651                    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