standards for successful project management.

$4.$A project designed to refurbish a hospital operating theatre consists of the following activities, with estimated times and precedence relationships shown. Using this information draw a network diagram, determine the expected time and variance for each activity, and estimate the probability of completing the project within sixty days.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$],[$s$]],\backslash$table$[[$Optimistic$],[$Time$]],\backslash$table$[[$Most Likely$],[$Time$]],\backslash$table$[[$Optimistic$],[$Time$]]],[$A$,-,5,6,7],[$B$,-,10,13,28],[$C$,$A$,1,2,15],[$D$,$B$,8,9,16],[$E$,$B$,$ C$,25,36,41],[$F$,$D$,6,9,18]]$

An activity has these time estimates: optimistic time $o=15$ weeks, most likely time $m=20$ weeks, and pessimistic time $p=22$ weeks.

a$)$ calculate the activity's expected time or duration $t.$

b$)$ calculate the activity's variance $v.$

c$)$ calculate the activity's standard deviation.