If men's heights are normally distributed with mean 68 and standard deviation 3.1 inches, and women's heights are normally distributed with mean 65 and standard deviation 2.8 inches, if a random man and random woman are chosen, find the probability that the woman is taller than the man.

the probability that the woman is taller than the man is  0.1423

Step-by-step explanation:

Given that :

the men's heights are normally distributed with mean  68

standard deviation   = 3.1

And

the women's heights are normally distributed with mean  65

standard deviation   = 2.8

We are to find the probability that the woman is taller than the man.

For woman now:

mean   = 65

standard deviation = 2.8

= 1-P (z , 1.07)

Using z table,

= 1 - 0.8577

= 0.1423

Thus, the probability that the woman is taller than the man is  0.1423

i just took the test, the correct answer is .. 31.5 in.