Westgate operates a coffee store at its lobby level. Daily use $($demand$)$ of ground coffee at the store has an average of $300$ pounds $($lbs$)$ with a standard deviation of $100$ lbs $($assume normal distribution$).$ Store manager orders $1000$ lbs of ground coffee, whenever $1600$ lbs of coffee left.$$ Order replenishment lead time is $4$ days.

$($a$)(8$ pts$)$ What fill rate does the store achieve with the current policy?

$($b$)(13$ pts$)$ If the store would like to have a $97\mathrm{.}5\%$ fill rate, what should the reorder point be$?$