Five automobiles of the same type are to be driven on a 300-mile trip. The first two will use an economy brand of gasoline, and the other three will use a name brand. Let X1,X2,X3,X4, and X5 be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with µ1 = µ2 = 20, µ3 = µ4 = µ5 = 24, and σ1 = σ2 = 4 for the economy brand. Define a random variable Y by

Y = (X1 + X2)/2 - (X3 + X4 + X5) / 3,

so that Y is a measure of the difference in efficiency between economy gas and premium gas. Compute P(0 <= Y) and P(-1 <= Y <= 1). [Hint: write Y = c1X1 + ... +c5X5.]