In the fall in the northern United States, a manufacturerof snowblowers makes the following advertised offer. If youpurchase a snowblower and then it snows less than 20% of averagethat winter you get a full refund of what you paid (and keep the snow blower). If it snows less than 50% average you get 50% of yourmoney back. (If it snows more than that you'll be glad youpurchased the snow blower!)
Assume here that the amount of snow is a random variable Xwhich may be approximated by a gaussian distribution with meanmx. Also assume that production costs on snowblowers are50%, distribution costs are 40%, and usual profit margins are 10%of the selling price of snowblowers. Determine the expected percentprofit to the company in the above conditions in this promotion if:
(a) σx = 0.2mx
(b) σx = 0.3mx