In: Math
1) A lawn and garden retailer operates 4 stores in the DFW Metroplex. One of its most popular items is a lawn tractor. Weekly customer demand is distributed N(10,52) at each store. Each store replenishes its stock to 15 lawn tractors at the start of each week. Note: Assume that weekly demands at each store are independent.
a) Consider just one store. What is the probability of a stockout in that store?
b) What is the probability of a stockout in at least two of the four stores?
c) Suppose that the four stores decide to pool their stock. Specifically, they decide to pool their weekly allocations (4 X 15 = 60) in a centrally located warehouse and draw from it as needed to satisfy their demand. How often will a store experience a stockout now?