The time estimate $($in weeks$)$ for the activities of a PERT network are given below.

$($a$)$ Draw the project network and identify all the paths through it$.$

$($b$)$ Determine the expected project length.

$($c$)$ Calculate the standard deviation and variance of the project length.

$($d$)$ What is the probability that the project will be completed.

$1.$ At least $4$ weeks earlier than expected time?

$2.$ No more than $4$ weeks later than expected time?

$($e$)$ If the project due date is $19$ weeks, what is the probability of not meeting the due date?

$($f$)$ The probability than the project will be completed on schedule if the scheduled completion time is $20$ weeks

$($g$)$ What should be the scheduled completion time for the probability of completion to be $90\%($Nov$./91)$