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The height of married men is approximately normal with mean 70 and standard deviation 3. The height of married women is approximately normal with mean 65 and standard deviation 2.5. What is the probability that a random married woman is taller than a random married man?
Hi,
Let M be a random variable = height of married man,
W be a random variable = height of married women.
Assiming that random variables M and W are independent, the random
variable X=M-W will be approximately normal with mean 70-65=5 and
standart deviation = square root of (3 squared + 2.5 squared)= 3.9...
We are interested in probability
P(X>0) = P(Z > (0 - 5)/3.9)=
P(Z > -1.28)
Using the normal distribution tables this is 0.8997.
Andrei
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