A Nike import distribution center $($hereafter refers to as IDC$)$ supplies a certain product to a Nike online fulfillment center $($hereafter referred to as OFC$).$ The manager at OFC estimates that the demand for this product follows a normal distribution with an average demand of $100$ per day and standard deviation of $20$ per day. The manager also estimates that for a $1\%$ increase $($or decrease$)$ in service level $($during the lead time$),$ the average annual sales will increase $($or decrease$)$ by $0\mathrm{.}1\%.$ The rest of the information regarding this product are listed below:

Average daily demand: $100$ units per day

Standard deviation of demand: $20$ units per day

Cost of goods sold at OFC: $$100$ per unit.

Product margin: $$10$ per unit.

Inventory carrying cost percentage: $30\%$ for all inventory $($either at IDC, OFC, or in$-$transit$).$

Order cost at OFC: $$100$ per order.

Current lead time from IDC to OFC: $5$ days

Assuming the manager in OFC uses a re$-$order point inventory control policy.The IDC orders the product from an Asian manufacturer with a lead time of $15$ days. To minimize its shipping cost, IDC orders $5,000$ units each time. Assuming OFC keeps the same order behavior $($that is$,$ orders $4,000$ units each time from IDC and maintains a service level of $98\%).$ On the other hand, IDC needs to maintain a service level of $99\%$ during the lead time, what is the average inventory level at IDC alone?