A retailer of a seasonal product is determining the order quantity for the coming selling season. The retailer buys each unit at $10 and sells it at a price of $20. At the end of the selling season, the leftover inventory can be sold at a discount price of $5 per unit. Demand follows a normal distribution with mean and standard deviation .

A stock-out takes place when the inventory is not enough to fill the demand. To maximize the expected profit, what should be the probability of stocking out for the retailer?