A supplier sells a popular auto part to car dealers. The weekly demand is approximately normal with the historical distribution of D~N$(63,25)$ units over a $45-$week operating year. The supplier pays $$26$ for each unit and sells each for $$41.$ In addition, they estimate that the annual holding cost is $30$ percent of the unit's cost $($to the supplier$).$ It costs approximately $$25$ to place an order $($managerial and clerical costs$).$ Assume a four$-$week lead time.

What is the distribution of the demand during lead time