Dr$.$ Jack is in charge of the Springfield Hospital$$s Blood Center. Blood is

collected in the regional Blood Center $200$ miles away and delivered to Springfield by air$-$

plane. Dr$.$ Jack reviews blood reserves and places orders every Monday morning for deliv$-$

ery the following Monday morning. If demand begins to exceed supply, surgeons postpone

nonurgent procedures, in which case blood is back$-$ordered.

Demand for blood on every given week is normal with mean $100$ pints and standard

deviation $34$ pints. Demand is independent across weeks.

a$.$ On Monday morning, Dr$.$ Jack reviews his reserves and observes $200$ pints in on$-$hand

inventory, no back orders, and $73$ pints in pipeline inventory. Suppose his order$-$up$-$to

level is $285.$ How many pints will he order?