$1.$ Weekly demand for laptops at a computer retail store is normally distributed with a mean of $500$ and a standard deviation of $220.$ The supplier takes two weeks to supply a retail store order. The store manager is considering following a periodic review policy to manage inventory of laptops. She plans to order every three weeks.

If the store manager wants to keep its $97$ percent cycle service level, how much safety inventory should the store carry? $(10$ points$)$

What should be its base$-$stock level be$?$