An Internet retailer stocks a popular electronic toy at a warehouse. Every week, the retailer decides how many units of the toy to stock. Suppose that the weekly demand for the toy is approximately normally distributed with a mean of 2500 units and a standard deviation of 300 units.
a) What is the probability that the weekly demand will be between 2255 and 2850 units?
b) If the retailer has 2750 units on hand at the start of the week, what is the probability that the weekly demand will be greater than the inventory?
c) If the retailer wants to limit the probability of being out of stock of the electronic toy to no more than 7% in a week, how many units should the warehouse stock?