Five automobiles of the same type are to be driven on a 300-mile trip. The first two wil...

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 independent and normally distributed with and σ² = 4 for the economy brand and 3.5 for the name brand. Define an rv Y by

so that Y is a measure of the difference in efficiency between economy gas and name-brand gas. Compute P(0 ≤ Y) and