$1.$b$)$ Boeing Renton Factory located in Washington, provides a particular part for Boeing $737$ aircrafts. Annual demand for this part follows a Poisson distribution with parameter $=1\mathrm{.}8$ units per year. The lead time for this part is $4$ months. What is the minimum base stock level that guarantees no stockouts in $98\%$ of the cycles? What are the expected backorder and inventory levels associated to this base stock level? For problem $1.$b$,$ show the evolution of inventory for the base stock level you found in a diagram.

$[25$ marks$]$