HW#$2$

Consider the network described in the table below.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$($s$)]],$Pessimistic,Probable,Optimistic$],[$J$,-,15,10,8],[$K$,-,9,8,7],[$L$,$J$,10,6,5],[$M$,$J$,3,3,3],[$N$,$K$,$M$,9,5,1],[$O$,$K$,$M$,10,7,4],[$P$,$L$,$N$,10,8,3]]$

a$.$ Calculate the expected duration of each activity.

b$.$ Calculate the expected duration and variance of the critical path.

c$.$ Calculate the probability that the project will be completed in fewer than $30$ time units.

d$.$ What time corresponds to when the top $30\%$ of those complete the project?