1. A solar panel salesperson claims that an array of solar panels on the roof of T'Chaka's Lodge will generate daily power that follows a normal distribution, with mean 6000 kilowatts and standard deviation 1400 kilowatts.Using these claims, calculate a number of kilowatts X such that the solar array will generate power output greater than X on 80% of days (and less than X on 20% of days).
2. Based on the claims of the solar panel salesperson, what is the probability that T'Challa will generate over 49,000 kilowatts during any given week (as before, let's go with the assumption that weather on different days are independent of each other)?
3. Assuming that the standard deviation of daily power from the proposed array is 1400 kilowatts, but the mean is unknown, what is the smallest sample that T'Challa needs to take in order to get a 95% confidence interval for the average daily power generation with a margin of error less than 250 kilowatts.