Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of the order placement, demand is still uncertain: Teddy Bower forecasts that its demand is normally distributed with a mean of 2100 and a standard deviation of 1200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity (and also doesn’t collect a tax benefit for the donation).
a. What is the probability this parka turns out to be a “dog,” defined as a product that sells less than half of the forecast?
b. How many parkas should Teddy Bower buy from TeddySports to maximize expected profit?