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. Â
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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