Consider comparing a decentralized versus a centralized inventory system as it ultimately relates to the amount of salety stock $($extra inventory over and above mean demand$)$ held in the system.

Focus on one specific part: SurgeArrester. The lead time for this part from manufacturing to warehouses is one week. Suppose that the CEO of ElectroWorks requires a $99\%$ customer service level. This means that the probability of satisfying customer demand during the lead time is $0\mathrm{.}99.$ Assume that lead time demands for the Milwaukee warehouse, Chicago warehouse, and centralized warehouse are Normally distributed with the following means $$ and standard deviations $$ :

$x=$ Milwaukee warehouse $,{}_x=415$ units $,{}_x=48$ units

$Y=$ Chicago warehouse $,{}_Y=2689$ units $,{}_Y=272$ units

Correlation between $x$ and $Y,=0\mathrm{.}52$

$x+Y=$ centralized warehouse $,{}_{x+Y}=3104$ units $,{}_{x+Y}=299\mathrm{.}78$ units

$($Use decimal notation. Use Table A$.$ Round your answer to the nearest integer.$)$