$[$Q $6-10]$ A newly created NorthEast Airways $($NE$)$ flight from Philadelphia to Boston has $300$ seats. The high fare on the flight is $$800$ and the restricted low fare is $$300.$ There is ample demand for the low fare class but high fare demand is random. Furthermore, the customers who buy low fare buy their tickets well in advance before high fare customers. Assume the demand for the high fare is normally distributed with a mean $120$ and a standard deviation of $50.$Mr$.$ Wright is in charge of the flight booking operations and decides to set a protection level for the high fare. What is the optimal protection level for the high fare?