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why do we use normalization coefficient in the central limit theorem?

For CLT we use $\sqrt{n}$ as the normalization factor, but why do we need it?

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  • $\begingroup$ I found the duplicates by searching our site. One helpful key word was "standardize." Please link to that search for further information. $\endgroup$
    – whuber
    Nov 5 '18 at 13:52