Ariana's Drug Store uses large quantities of Zac's Body Wash, on average $750$ per week with a standard deviation of $120.$ The lead time is three weeks and they have a lot size of $24$ bottles. $(10$ total points$)$

a$.$ What is the standard deviation of demand during their lead time?

b$.$ Suppose Ariana sets her reorder point at $3250$ bottles. What is her average bottle inventory and safety stock? $(4)$

c$.$ What is the average flow time Ariana uses $5000$ as the reorder point?