Morty Seinfeld's Raincoats is a major rainwear catalog company in greater Manhattan, and they are planning to launch a new line of high$-$end raincoats, Executive, for this year's rainy season. The demand for raincoats is highly seasonal and occurs only in the months of apr$-$jun, but the manufacturing of these raincoats require careful attention. As a result, Morty has to start planning the production of these coats about a year befor the rainy season starts. During this time, Morty has only limited information of the demand and he has to decide the production quantity early using his limited information. Specifically, it is known that the demand for Executive will be a normal distribution with a mean of $20,000$ units and a standard deviation of $10,000.$ During the season, Morty sells each of these coats for $$300/$raincoat and the production cost is $$100/$raincoat$.$ In addition, any raincoats that are not sold at the end of the rainy season can be sold to a discount retailer in Seattle. Since it rains all through the year in Seattle, raincoats are always in demand in there, and Morty would be able to sell all his excess stock at a price of $$75/$raincoat$.$ However, it costs Morty $$25/$raincoat to ship each of these raincoats to Seattle. Using the information above, Morty wants you to help him decide the production quantity for the rainy season. On average how many raincoats would morty sell during the rainy season?