The Gilbert Air-Conditioning Company is considering the purchase of a special shipment of portable air conditioners manufactured in Japan. Each unit will cost Gilbert $80, and it will be sold for $125. Gilbert does not want to carry surplus air conditioners over until the following year. Thus, all surplus air conditioners will be sold to a wholesaler for $50 per unit. Assume that the air conditioner demand follows a normal probability distribution with μ 5 20 and σ 5 8.
a. What is the recommended order quantity?

b. What is the probability that Gilbert will sell all units it orders?