Question $5,(2$ Marks$)$:

Ottawa$$s Fairmont hotel distributes, on average, $1000$ bath towels per day to their guests at the pool and within their hotel rooms. This demand is normally distributed with a standard deviation of $100$ towels per day, depending on occupancy. The laundry service firm $(3$rd party contract$),$ promises a $2$ day lead time to wash and return$/$restock the towels when needed. The hotel aims for a $98\%$ service level to its customers to ensure satisfied customers.

a$)$ Determine the ROP for this hotel?

b$)$ What should be the safety stock quantity in order to sustain the service level?