$1.$ Given the project information below, answer the following questions:

Activity Predecessor Optimistic Time $($a$)$ Most Likely Time $($m$)$ Pessimistic Time $($b$)$ Expected Time $($Te$)$ Variance

A None $31227$

B None $82026$

C A $4716$

D A$,$ B $273045$

E C$,$D $101316$

Using PERT method and based on expected time $($Te$)$ for each activity, determine the expected project duration $($rounded to whole numbers$).$

$2.$ C$7$Q$2$ is based on the same information as presented for C$7$Q$1$

Given the project information below, answer the following questions:

Activity Predecessor OptimisticTime $($a$)$ MostLikely Time $($m$)$ PessimisticTime $($b$)$ ExpectedTime $($Te$)$ Variance

A None $31227$

B None $82026$

C A $4716$

D A$,$ B $273045$

E C$,$D $101316$

Question C$7$Q$2$:

What is the probability of completing the project in $58$ periods? Fill a decimal value in the blank below $($Note: rounded to $4$ decimals