The normal distribution is one common way that natural data can shake out, and one that CAN be a fair assumption IF AND ONLY IF you don’t have reason to believe it will be otherwise. Consider some alternatives:
* How is height distributed? Well, for adult males it’s normal, and for adult females it’s normal, but for all adults it’s bimodal (two-humped) because the average man is taller than the average woman. Add in children and you’ll have a skewed distribution.
* How is wealth distributed? Some nations will have a strong concentration of wealth in the hands of a few, showing strong skewing. Others will have a more even distribution. Regardless, there’s no guarantee that the middle class will be large enough to ensure a nice symmetric normal distribution, or that there will be as many rich people as poor people. Of course, unless we count debt as negative wealth, you can’t have less than zero dollars, but you can have as many billions as you can make, so it will also have a long tail.
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