$)$: A local tech store sells on average $500$ phone cases weekly with a standard deviation of $200.$ Assume the demand is normally distributed. Replenishment lead time is $2$ weeks. The store is targeting a service level of $95\%$ and uses a periodic review policy under which it reorders cases every $8$ weeks.

$($a$)(5$ pts$)$ What is the average order size?

$($b$)(10$ pts$)$ How much safety inventory should the store carry? What should order$-$up$-$to level be$?$