How can i establish that for each $$p \in [0,1] $$ if $$X_{1},X_{2}...$$ are a coin runs to parameter p, with the propability P to cover up the confidence region $$R:=\left[\overline{X}_n-\frac{\sqrt{5}}{\sqrt{n}}, \overline{X}_n+\frac{\sqrt{5}}{\sqrt{n}}\right]$$ with Chebyshev inequality: $$P((\overline{X}_n-EX) \ge c\sigma) \le \frac{1}{c^2}$$ not less than .95!
I start with
$$=> $$ $$P((\overline{X}_n-EX) \le c\sigma) \ge 1 - \frac{1}{c^2} \ge 0.95 $$
$$P(\overline{X}_n-\frac{\sqrt{5}}{\sqrt{n}}\le p \le \overline{X}_n+\frac{\sqrt{5}}{\sqrt{n}}) = 0.95$$
$$1-\frac{1}{c^2} = 0.95$$ $$c=2\sqrt{5}$$
From here I am stuck...