The following table represents a project that should be scheduled using CPM:

Time $($Days$)$

Activity Immediate Predecessors Optimistic Most Likely Pessimistic

A $-135$

B $-123$

C A $123$

D A $234$

E B $3411$

F C$,$ D $345$

G D$,$ E $146$

H F$,$ G $245$

$($a$)$ Draw the network. $(5$ points$)$

$($b$)$ What is the critical path? $(5$ points$)$

$($c$)$ What is the probability of completing this project within $16$ days? $(5$ points$)$