You are working on a programming project with your partner for a computer science course. The project is due in $48$ hours. Together, you are to produce a computer program and each of you are assigned to write a portion of computer code. Both of you work simultaneously, but independently. The completion time of your task follows a uniform distribution between $30$ and $50$ hours. Your partner is stronger in programming and his task is more complex, and the completion time for his task follows a uniform distribution between $35$ and $56$ hours.

Part a$)$ What is the expected completion time $($in hours$)$ for your partner's task?

A$.51\mathrm{.}5$

B$.53$

C$.48$

D$.45\mathrm{.}5$

E$.40$

Part b$)$ What is the corresponding standard deviation for the completion time of your partner's task?

A$.1\mathrm{.}32$

B$.2\mathrm{.}81$

C$.36\mathrm{.}75$

D$.15\mathrm{.}77$

E$.6\mathrm{.}06$

Part c$)$ What is the probability that you and your partner are not able to hand in your project on time $($that is$,$ your team's project completion time exceeds $48$ hours$)?$

A$.0\mathrm{.}6823$

B$.0\mathrm{.}4888$

C$.0\mathrm{.}4429$

D$.0\mathrm{.}5455$

E$.0\mathrm{.}5200$

Part d$)$ On the $48$th hour when the project is due, you and your partner have not completed the project. You approach the course instructor for an extension. The course instructor grants you and your partner an extension of $4$ hours to hand in the project starting from the $48$th hour. What is the probability you and your partner are now able to meet the new deadline?

A$.0\mathrm{.}5699$

B$.0\mathrm{.}4375$

C$.0\mathrm{.}3175$

D$.0\mathrm{.}6888$

E$.0\mathrm{.}775$