A small copy center uses five $500-$sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of five boxes per week and a standard deviation of one$-$half box per week. Two weeks are required to fill an order for letterhead stationery.

If the copy center reorders when the supply on hand is $12$ boxes, what is the risk of a stockout? $($Please keep $4$ digits after the decimal point.$)$ weeks are required to fill an order for letterhead stationery.

If the copy center wants to have a stockout rate that is no more than $1\%,$ what should be the reorder point?

If a fixed interval of seven weeks instead of an ROP is used for reordering, what risk does the copy center incur that it will run out of stationery before this order arrives if it orders $36$ boxes when the amount on hand is $12$ boxes? $($Please keep $4$ digits after the decimal point.$)$

To reduce the inventory cost, the company decides to shorten the FOI review cycle from $7$ weeks to $4$ weeks. What will be the order quantity if the on hand inventory is $12$ box at the review time if we maintain the service level as the same?

To reduce the inventory cost, the company decides to shorten the FOI review cycle from $7$ weeks to $4$ weeks. What percentage of inventory holding cost can be saved if it maintains the same service level?