A woman insists that she will never marry a man as short as or shorter than she, knowing that only one man in 400 falls into this category. Assuming a mean height of 69 inches for men with a standard deviation of 2.5 inches (and a normal distribution), approximately how tall is the woman?

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Lewis549id Lewis549id

Mathematics

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A woman insists that she will never marry a man as short as or shorter than she, knowing that only one man in 400 falls into this category. Assuming a mean height of 69 inches for men with a standard deviation of 2.5 inches (and a normal distribution), approximately how tall is the woman?

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Dzyid Dzyid · Answer 1

The woman is 61.5 inches tall.

This question is essentially asking for how many standard deviations the woman's height is away from the mean men's height.

Only 1 in 400 (or 0.25%) of men is shorter than our picky homegirl. If you think of a normal distribution of men's heights, this is the extreme left tail end. As a rule of thumb, +/- 3 standard deviations around the mean captures 99.5% of a population, leaving 0.5% outside of the interval (so, only 0.25% on each end). So we know that our girl refuses to marry anyone lower than -3 standard deviations from the mean.

All that's left is to plug in the given mean and SD:

69 -3(2.5) = 61.5 inches