Problem $3$

For the project in Problem $2,$ assume the task times are variable, with the optimistic, most likely, and pessimistic task times as follows:

TASK TIME $($DAYS$)$ TASK DESCRIPTION OPTIMISTIC MOST LIKELY PESSIMISTIC A Inspect the house $245$ B Appraise the house $135$ C Do the title search $346$ D Get the tax clearance $3510$ E Get the sales permit $122$ F Find a buyer $72142$ G Get a mortgage $71430$ H Get the legal documents $51014$ I File the legal documents $111$ J Final closing $111$

a$.$ Compute by hand the earliest expected completion time of the project, identify the critical tasks and path$($s$),$ and determine the variance of the project's completion time. $(10$ points$)$

b$.$ Use Excel QM to verify your computations in part $($a$).(5$ points$)$

c$.$ What is the probability of selling a house within $55$ days? $(4$ points$)$

d$.$ Home Sellers wants to complete $97\mathrm{.}5\%$ of its home sales within a certain time. What is that time $($to the nearest day$)?(6$ points$)$