# Central Limit Theorem question

$$f(x)=\left\{\begin{matrix} 2-2x & 0\leq x\leq1 \\ 0 & else \end{matrix}\right.$$

Let $Z$ be a standard normal random variable. Use the Central Limit Theorem to find the number $a$ so that

$$\lim_{n\rightarrow \infty}P\left ( \frac{1}{n} \sum_{i=1}^{n} X_i\leq\frac{1}{3}+\frac{2}{\sqrt n} \right ) = P(Z\leq a) $$

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