In a certain village, the heights of the women are normally distributed with a mean of 164

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In a certain village, the heights of the women are normally distributed with a mean of 164 cm and a standard deviation of 5 cm. The heights of the men are normally distributed with a mean of 173 cm and a standard deviation of 6 cm. A man and a woman are picked at random from the people in the village. Find the probability that

(a) the woman is taller than the man,

(b) the man is more than 5 cm taller than the woman.

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