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 1
2
20, 3
4
5
21, and 2
4 for the economy brand and 3.5 for the name brand.

Define an rv Y by Y


so that Y is a measure of the difference in efficiency between economy gas and name-brand gas. Compute P(0  Y) and P(1  Y  1). [Hint: Y
a1X1 . . . a5X5, with a1

2 1

, . . . , a5


1 3

.]