Use the following problem statement to answer questions $1-6.$

BK Home, a homebuilding company, plans to build a new shopping center. A consultant for the company has constructed a project network and estimated activity times, in weeks. The consultant found the following critical path: $ACD.$ The expected activity times of $A,C$ and $D$ are $7,5,$ and $4$ weeks. The variances of $A,C$ and $D$ are $3,2,$ and $2.[$Note: $z=\frac{x-t}{}$

$4$ Multiple Choice $4$ points

What is the expected project completion time?

$4$

$16$

$$ Multiple Choice

$4$ points

What is the standard deviation of the project completion time? Round to four decimal places.

$0\mathrm{.}9999$

$1\mathrm{.}0000$

$2\mathrm{.}6458$

$$ Multiple Choice $4$ points

What is the probability the project can be completed within $19$ weeks?

$37\mathrm{.}08\%$

$87\mathrm{.}08\%$