Suppose that a software development project team has arrived at the following time estimates for a software project.

Tasks and Task durations $($days$)$:

Design Software Nor$(20,5)$

Develop Interface Nor$(50,10)$

Develop Engine Nor$(55,10)$

Start Manual Nor$(20,5)$

Begin Phase $2$ Nor$(2,0\mathrm{.}5)$

Test$/$Debug Nor$(20,5)$

Finish Manual Nor$(20,5)$

Produce$/$Release Nor$(30,8)$

where each task uses a Normal$($mean$,$ SD$)$ distribution.

a$.$The duration of each task is described by a normal statistical distribution. If the duration of each task was precisely the mean of this distribution, what would the project duration be$?$

b$.$Report the overall mean duration of the project from $300$ simulations of the model $($using the statistical distributions and SimQuick$).$ How does this number compare with the duration reported in part a$?$

Note: Project duration $=(1$ mean inventory of End$)*($Simulation duration$)$