Sellen Construction $[$HANDWRITTEN SUBMISSION WILL NOT BE GRADED$].$

Sellen Construction is negotiating a deal with Countryside Realtors to build six houses in a new development. Countryside wants Sellen to start in late winter or early spring when the weather modifies and builds through the summer into the fall. The summer months are busy for the realty company, and it believes it can sell houses almost as soon as they are ready, sometimes before. The houses have similar floor plans and are approximately the same in size; only the exteriors are noticeably different. The completion time is so critical for Countryside realtors that it is insisting that a project management network accompany the contractor's bid for the job with an estimate of the completion time for a house. The agent also needs to plan its offerings and marketing for the summer. The realtor wants each house to be completed within $43$ days of the starting date. If a home is not completed within this time frame, the realtor wants to be able to charge the contractor a penalty. The Sellen is concerned about the prospect of a penalty. They want to be confident they can meet the house's deadline before entering into any agreement with a penalty.

Sellen has experience building houses, so it was not difficult to list the activities involved in building a house or estimate activity times. However, they made their estimates conservatively and tended to increase their pessimistic estimates to compensate for the possibility of bad weather and variations in their workforce. Table $1$ lists the activities and the estimated activity times.

QUESTION $1.$ Show the answer to the following questions.

a$.$ The network diagram.

b$.$ The expected completion time for all paths $($keep two decimals$).$

c$.$ Identify the critical path.

d$.$ The standard deviation and the $\backslash ($ Z $\backslash )$ value.

e$.$ The probability of completing the project in $44$ days or less.

TABLE $1$ Time $($Days$)$