The weights of hamburgers have a normal distribution with mean 105 grams and standard deviation 7.5 grams. Hamburgers weighing less than 100 grams are sold as "specials" for $2.00, while those over 125 grams are sold as "bonus burgers" for $2.80. The remaining hamburgers are used for regular burgers, selling for $2.50.

(a) (7 points) Assume all sizes of hamburgers can be sold. Find the average selling price for a hamburger.

(b) (3 points) Calculate the probability that the total weight of 2 randomly chosen hamburgers exceeds 225 grams.

(c) (4 points)Find the approximate probability that a shipment of 150 hamburgers will contain at least 40 suitable for use as "specials".