As in Exercise 24 and Example 36 10 assume that the height (in inches) of an American female is Normal with expected value 64 and standard deviation 1 2 5 Also assume that the height of an American male is Normal with expected value 2 69 and standard deviation 2 3 0 A man and a woman are chosen at ...

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As in Exercise 24 and Example 36.10 assume that the height (in inches) of an American female

Question:

As in Exercise 24 and Example 36.10 assume that the height (in inches) of an American female is Normal with expected value μ = 64 and standard deviation σ1 = 2.5. Also assume that the height of an American male is Normal with expected value μ2 = 69 and standard deviation σ2 = 3.0.
A man and a woman are chosen at random. The woman's height is measured, and she is found to be exactly 68.2 inches tall. How much taller do we expect the man to be (as compared to this particular woman)?