Very difficult question and I do not understand. Please help.

Problem 3: Power Grid (90 points) A town receives its electrical power supply from 10 nearby plants. It has been empirically de- termined the town needs 20 units of power per day in order to prevent shortage. For each day, suppose each power plant has p probability of operating and 1 fp probability of being down for maintenance. The amount of power generated by a given plant per day (X) is independent of the number of plants operating that day and is normally distributed with gr 2 5 and 0'2 = 5. Assume the power supplied to the town per day P is just the sum of the power generated by each plant. 1. Find E [P] in terms of p 2. Find Var(P) in terms of p 3. To minimize the risk of power shortage, E [P] needs to be at least 3 standard deviations (0p) greater than the daily demand. Find the maximum probability of plant failure q = 1 p to meet this target. Round to 3 decimal places. (Note Feel free to plot and estimate here. You don't need to solve exactly!)