The Kwik$-$E$-$Mart can sell a box of fresh donuts for $$16,$ which is a tidy sum since the store only spent $$12$ to produce that box. Homer has agreed to take any unsold boxes of donuts at the end of every day for $$7$ because even old donuts are still donuts.

The daily demand for boxes of fresh donuts has a normal distribution of $53,$ with a standard deviation of $13.$

What is the under$-$stocking cost Cu$?$

What is the over$-$stocking cost Co$?$

What is the critical fractile? Please state your answer as a number between $0$ and $1,$ round to $4$ decimal places.

What is the corresponding z$-$score?

How many boxes of fresh donuts should the Kwik$-$E$-$Mart stock every morning? Enter a whole number$$don$\text{'}$t use fractions or decimals. Round up$,$ round down, or whatever you like.