Suppose that when an oil company drills a well, there is a 15% chance that it will produce oil. Assume that the outcomes of the drillings are independent and the company drills 12 wells.

(a) Find the mean and standard deviation of the number of successful wells.

(b) Find the probability that at most 3 wells produce oil.

(c) Suppose the company has fixed costs of $28,000 for the entire drilling project, each productive well costs $24,000 to drill, and each unproductive well costs $15,000 to drill. Write the function that expresses the total cost of drilling x successful wells and find the company’s expected total cost for the 12 wells.