Bob Smith is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier. Unfortunately, at the time the order is placed, demand is still uncertain. Bob Smith forecasts that its demand is normally distributed with a mean of 2,100 and a standard deviation of 1,200. Bob sells the parkas for $22 each. Unsold parkas have little salvage value and are donated to charity.
a. What is the probability that this parka sells less than half of its mean forecast?
b. How many parkas should Bob Smith order to maximize its expected profit?
c. If Bob Smith wants to target a 98.5% in-stock probability, then how many parkas should it order?
d. If Bob Smith orders 3,000 parkas, determine its expected profit.
e. If Bob Smith orders 3,000 parkas, determine its stockout probability.