John Doe Enterprises utilizes a continuous review inventory system. Whenever inventory position falls to $250$ unites, an order for $1,000$ additional units is placed. Lead time for the product is $2$ weeks. Average weekly demand is $75$ units; however, demand is known to fluctuate widely. Standard deviation of weekly demand is $45$ units.

a$.$ What service level is John Doe Enterprises maintaining?

b$.$ John Doe has decided to maintain no safety stock inventory. With what probability will the company stock out during ay given inventory cycle? Show how you arrived at your answer.