The answer is that 84% of women are taller than 62 inches .
The given problem is a problem of normal distribution in mathematical statistics. This distribution is a continuous univariate distribution. Its density function is given by -
f(x)= [tex]\frac{1}{σ\sqrt{2\pi } }[/tex][tex]e^{\frac{-1}{2} }[/tex]([tex]{\frac{x-u}{σ}}^{2}[/tex])
Now the actual question is what proportion of women are taller than the height at one standard deviation below the mean since that is the first quartile range.
Following the statistical rules of the normal distribution, we know that 50% of women are taller than the mean height of 64.5 inches.
In addition to this, we know that 34% of women will have heights of between minus 1 standard deviation and the mean (62 and 64.5 inches). Adding these percentages together, we can determine that 84% of women are taller than 62 inches or minus 1 standard deviation.
Hence, 84% of women are taller than 62 inches or minus 1 standard deviation.
Please find the attached image.
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