Question $2\mathrm{.}3$

Consider the network described in the table below.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Activity & Immediate Predecessor$($s$)$ & Pessimistic & Probable & Optimistic $\backslash \backslash$

$\backslash$hline J & $--$ & $15$ & $10$ & $8\backslash \backslash$

$\backslash$hline K & $--$ & $9$ & $8$ & $7\backslash \backslash$

$\backslash$hline L & J & $10$ & $6$ & $5\backslash \backslash$

$\backslash$hline M & J & $3$ & $3$ & $3\backslash \backslash$

$\backslash$hline N & K$,$ M & $9$ & $5$ & $1\backslash \backslash$

$\backslash$hline O & K$,$ M & $10$ & $7$ & $4\backslash \backslash$

$\backslash$hline P & L$,$ N & $10$ & $8$ & $3\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Draw the network diagram and answer the following questions.

$($a$)$ Calculate the expected duration of each activity.

$($b$)$ Calculate the expected duration and variance of the critical path.

$($c$)$ Calculate the probability that the project will be completed in more than $28$ time units.