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Management Decision Systems $($MDS$)$ is a consulting company that specializes in the development of decision support systems. MDS has a four$-$person team working on a current roject with a small company to set up a system that scrapes data from a collection of websites and then automatically generates a report for management on a daily basis.

$\backslash$table$[[,$Time $($Weeks$),],[$Activity$,$Description,$\backslash$table$[[$Immediate$],[$Predecessor$]],$Optimistic,Most Probable,Pessimistic$],[$A$,$Report generation,,$1,8,12],[$B$,$Web scraping,,$5,9,11],[$C$,$Testing,A$,$ B$,1,1,1]]$

$($a$)$ Construct the project network. $($Submit a file with a maximum size of $1MB.)$

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b$)$ Based solely on the critical path, estimate the probability that the project will be complete within $11$ weeks. $($Round your answer to four decimal places.$)$

c$)$ Using all paths through the project network, estimate the probability that the project will be complete within $11$ weeks. $($Round your answer to four decimal places.$)$

d$)$ Should you use the estimate in $($b$)$ or $($c$)?$

The probability estimate from $($b$)$ based on the critical path is more accurate.

The probability estimate from $($c$)$ based on both paths is more accurate.

The probability estimates from $($b$)$ and $($c$)$ are equal.