SOLUTION: Here is my problem that I am working through on probabilities of random variables. Suppose heights of men in inches follow a N(71,3) model and heights of women follow a N(67, 2.5)

Question 102622: Here is my problem that I am working through on probabilities of random variables. Suppose heights of men in inches follow a N(71,3) model and heights of women follow a N(67, 2.5) model. If I randomly choose a man and randomly choose a woman, what's the probability that the woman will be taller than the man?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose heights of men in inches follow a N(71,3) model and heights of women follow a N(67, 2.5) model. If I randomly choose a man and randomly choose a woman, what's the probability that the woman will be taller than the man?
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If you randomly choose a man his height will be 71 inches.
You want the probability a randomly selected woman's height is greater
than 71 inches.
z(71)= (71-67)/3 = 4/3
Prob(z>4/3) = 0.091
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Cheers,
Stan H.
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