The Global Tea and Organic Juice companies have merged. The following information has been collected for the "Consolidation Project."

page $253$

$\backslash$table$[[$Activity$,$Description,Predecessor,a opt,$m$ ml$,b$ pess$],[1,$Codify accounts,None,$16,19,28],[2,$File articles of unification,None,$30,30,30],[3,$Unify price and credit policy,None,$60,72,90],[4,$Unify personnel policies,None,$18,27,30],[5,$Unify data processing,$1,17,29,47],[6,$Train accounting staff,$1,4,7,10],[7,$Pilot run data processing,$5,12,15,18],[8,$Calculate P & L and balance sheet,$6,7,6,12,24],[9,$Transfer real property,$2,18,27,30],[10,$Train salesforce,$3,20,35,50],[11,$Negotiate with unions,$4,40,55,100],[12,$Determine capital needs,$8,11,20,29],[13,$Explain personnel policies,$11,14,23,26],[14,$Secure line of credit,$9,12,13,16,19],[15,$End,$10,13,14,0,0,0]]$

Compute the expected time for each activity.

Compute the variance for each activity.

Compute the expected project duration.

What is the probability of completing the project by day $112?$ Within $116$ days?