QUESTION $3(1\mathrm{.}50$ points$)$

Conrad Weitzel considers himself a conservative project manager, so he never accepts deadlines that provide a safety margin below $85\%.$ The Project Management software used by your company estimates a new project has an average duration of $40$ weeks and a standard deviation of $2\mathrm{.}5$ weeks. Given Mr$.$ Weitzel's assumption, what would the most appropriate duration for the project be$?$

QUESTION $4(1\mathrm{.}50$ points$)$

A project by Thomas Weber has an expected duration of $40$ weeks and a variance of $25$ weeks ${?}^2.$ The project duration is assumed to be normally distributed.

a$)$ What is the probability of completing the project in $50$ weeks or less? $(0\mathrm{.}50$ point$)$

b$)$ What is the probability of completing the project in $38$ weeks or less? $(0\mathrm{.}50$ point$)$

c$)$ What duration would give Thomas a $98\%$ chance that the project is finished by that time?

$(0\mathrm{.}50$ point$)$