The sources of electrical power for a region nuclear, fossil, and hydroelectric. The respective generating capacities of these sources can be described as independent Gaussian random variables as follows (in megawatt power): Nuclear: N (100,15) Fossil: N (200,40) Hydro: N (400,100) (a) Determine the total power supply for the region; i.e., define the probability distribution of the power supply with the corresponding mean and standard deviation. (b) The power demand of the region during normal weather is 400 megawatts, whereas during extreme weather the demand would be 600 megawatts. In any given year, normal weather is twice as likely to occur as extreme weather. With the generating capacity of (a), what is the probability that power shortage for the region will occur during the year?