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Every month, the government of Neverland spends X million dollars purchasing guns, Y million dollars purchasing butter, and saves Z million dollars. Assume X, Y, and Z follow a multivariate normal distribution with parameters : μx = 385, μy = 300 μz = 155, σx = 40, σy = 44, σz = 46, and correlations of ρxy = -0.23, ρxz = -0.36, and ρyz = 0.35.
a) Suppose the government of Neverland spent 450 million dollars on guns and 200 million on butter during a particular month. Find the probability that more than 150 million was saved during the same month
b) Find the probability that the government of Neverland exceeds the 800-million spending limit during a given month (consider spending as X + Y + Z)
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