29. Five automobiles of the same type are to be driven on a 300-mile trip. The rst 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 ef ciencies (mpg) for the ve cars. Suppose these variables are independent and normally distributed with m1  m2  20, m3  m4  m5  21, and s2  4 for the economy brand and 3.5 for the name brand. De ne an rv Y by so that Y is a measure of the difference in ef ciency between economy gas and name-brand gas.

Compute P(0 Y) and P(1 Y

1). (Hint: Y 

a1X1 . . .  a5X5,with .)