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

A project by Fernando Ferreira 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 Fernando a $98\%$ chance that the project is finished by that duration? $(0\mathrm{.}50$ point$)$