$4.(15$ points$)$ Below is a simple project. All durations are given in weeks.

Activity Immediate Predecessor Duration

Optimistic Most Likely Pessimistic

A $-345$

B A $5814$

C A $5919$

D B$,$C $6912$

Determine the critical path and answer the following:

a$)$ What is the probability the project will be completed in $25$ weeks or less?

b$)$ What is the probability the project will be completed in $20$ weeks or less?