Sums of Independent Random Variables

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Homework Statement



Let X be the height of a man and Y be the height of his daughter(both in inches). Suppose that the joint probability density function of X and Y is bivariatenormal with the following parameters: mean of X=71, mean of Y=60, std. deviation of X=3, Std. deviation of Y=2.7, and p(rho)=.45.Find the probability that the man is at least 8 inches taller than his daughter.



Homework Equations





The Attempt at a Solution



X=N(71,9); Y=N(60,7.29); X-Y=N(11,1.71)
P(X-Y>=8)=(8-11)/(sqrt(1.71))=-3/1.31=-2.29; I(-2.29)=.0110
The difficulty I am having here is determining when to apply the p(rho)=.45 factor.
Should I apply it to the .0110 probability, or do I apply it sometime earlier?

Assistance would be very much appreciated!
 
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