Problem $2$ PERT$/$CPM table is helene. Note that the Expected Time and Variance are calculated

Time Estimates

Activity

$17$

$400$

$1\mathrm{.}00$

$044$

Start

Finish

Problem $2(15$ points$)$:

The following page has a PERT$/$CPM set up which is partially completed, as well as the table of completed expected activity times and variances of time. Activity times are given in days. A z$-$table is appended to the end of this exam.

$($a$)$ State the critical path and the expected days for project completion. You must fill in the boxes in the chart on the following page. $(7$ points$)$

$1-3-5-7,$ Project expected to be completed in $24$ days.

$($b$)$ What is the probability that the project will be completed in $28$ days or less? $(8$ points$)$

$(1)$ Need V$($T$)=\backslash$sigma $^2=2+2+2+24+0\mathrm{.}44+0\mathrm{.}44+0\mathrm{.}11-4\mathrm{.}99$ days $(5$ days is acceptable$)$

$(2)$ From the critical path, p $=5($or $4\mathrm{.}99),\backslash$sigma $\backslash$epsi $=5,6=$ sqrt$(5)=2\mathrm{.}24$

$(3)$ x$=28$

sqrt$(4\mathrm{.}99)2\mathrm{.}23$

$(4)$ Z$(28-24)/2\mathrm{.}23-1\mathrm{.}79$

z$-$table$=0\mathrm{.}4693$

$(5)$ Prob$($T$<=28)=0\mathrm{.}5000+0\mathrm{.}46930\mathrm{.}9633-96\mathrm{.}33\%$