A partially solved PERT problem is detailed in the table below. Times are given in weeks. $1.$ Calculate the expected time for each activity. Enter these values in the appropriate column in the table above. $2.$ Which activities form the critical path? $3.$ What is the estimated time of the critical path? $4.$ What are the project variance and the project standard deviation?$[[$Activity$,$Preceding,$[[$Optimistic$],[$Time$]],[[$Probable$],[$Time$]],[[$Pessimistic$],[$Time$]],[[$Time$],[$Timected$]],$Variance$],[$A$,-,6,7,12,,],[$B$,$A$,2,2,9,,],[$C$,$A$,7,9,14,,],[$D$,$A$,2,6,11,,],[$E$,$B$,3,5,9,,],[$F$,$B$,$ C$,5,7,10,,],[$G$,$C$,$ D$,$ F$,3,4,9,,],[$H$,$D$,$ G$,2,3,8,,],[$I$,$G$,$ H$,5,6,10,,],[$J$,$G$,$ I,$4,5,13,,],[$K$,$E$,$ F J$,2,2,11,,]]7.$ A partially solved PERT problem is detailed in the table below. Times are given in weeks. $(10$ points$)$

a$.$ Calculate the expected time and variance for each activity. Enter these values in the appropriate column in the table above.

b$.$ Which path$($s$)$ form the critical path?

c$.$ What is the estimated time of the critical path?

d$.$ What are the project variance and the project standard deviation?

e$.$ What is the probability of completion of the project within $31$ weeks?