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I need to show that the chi square distribution can be approximated through the central limit theorem to $\frac{(X-1)}{\sqrt{\frac{2}{n}}}$ ~ Normal (0,1),

where X=sample mean.

Knowing that $X^2=\frac{x^{\frac{n}{2}-1}e^\frac{-x}{2}}{gamma(\frac{n}{2})2^{\frac{n}{2}}}$ I can clearly relate it to the gamma distribution but I'm honestly just generally confused over how to go about this approximation. Any help greatly appreciated!

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    The same question was asked by another user at approximately the same time: http://math.stackexchange.com/questions/2146240/properties-of-the-central-limit-theorem-pertaining-to-the-chi-square-distributio – 2017-02-15

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