A ski jacket sells for $$350$ a piece and costs the mountain lodge retailer $$200$ to procure. Unsold jackets at the end of the season are sold online for $$150$ a piece. There is an average warranty cost to the retailer of $$50$ per jacket sold $($due to some customers returning the jackets$).$ This warranty cost is not incurred for the jackets sold online at the end of the season. Demand for the jackets can be assumed normally distributed with mean of $750$ and stdev of $125$ jackets over the season. The retailer can only order the jackets once, and a few months before the winter season begins at the lodge at that.

What is the optimal service level reported as a probability between $0$ and $1,$ for the ski jackets at the retailer?