Q$.4$ Construct a network so as to satisfy the scheduling requirements shown in the table below.

$\backslash$table$[[$Activity$,\backslash$table$[[$Preceding$],[$Activity$]],\backslash$table$[[$Duration in days$]],$Optimistic,$\backslash$table$[[$Most$],[$Probable$]],$Pessimistic$],[10,22,22,,,,],[$B$,-,20,20,20,,,,],[$C$,-,4,10,16,,,,],[$D$,$A$,2,14,32,,,,],[$E$,$B$,$C$,8,8,20,,,,],[$F$,$B$,$C$,8,14,20,,,,],[$G$,$B$,$C$,4,4,4,,,,],[$H$,$C$,2,12,16,,,,],[$I$,$G$,$H$,6,16,38,,,,],[$J$,$D$,$E$,2,8,14,,,,]]$

a$)$ Find the time required to complete the whole project and identify the critical activities.

b$)$ What is the probability that the project will be completed within $50$ days assuming nomal distribution?

c$)$ What deadline are you $98\%$ sure of meeting?

$(20)$