You are currently working for MyCar, a US manufacturer. Your main responsibility is managing the shipping of engins from your supplier in China to your company's factory in New Mexico.

Demand for the engins is normally distributed with an average of $120000$ engins per year and an annual standard deviation of $9600.$ MyCar currently purchases engins each year from the supplier at a price of $$113$ per unit.

The lead time for the delivery is $4$ days on average, with a standard deviation of $2\mathrm{.}5$ days. You use Carrier VEC, which charges $$6$ per engin, with a minimum shipment of $2000$ engin $($i$.$e$.,$ Q$=2000$ engins.$)$ Your company takes ownership of the shipment at the supplier$$s dock and will have to incur any holding costs from that point on$.$ Your company's annual holding charge is $13\%,$ a cycle service level of $95\%$ and uses a $365$ days per year for planning purposes.

Your company includes the cost of transportation in the cost of the motors when calculating inventory costs.

Part $1$

What is the expected demand $($in enginss$)$ over lead time? Round your answer to the nearest integer