Probability that total number of sixes in $n$ dice tosses Let X be the total count of fives in $n$ dice ups and downs s.t. it is in between  $\frac 1 k n +/- \sqrt n$  with k=6. Calculate Pr(X).


I personally think that I  should integrate the probability density function of n such that it is in between the two values? I dont know how to find that pdf but I know for n throws, you expect to get n/6 sixes. any hin would be helpful thanks!
Hint:


Let $Y \sim Bin(n, \frac16)$
Use Chebyshev's inequality on $Pr \left(|Y-\mathbb{E}(Y)|\ge \sqrt{n} \right)$
Hint: $P(a&lt; X\leq b) = P(X\leq b) - P(x\leq a) = F_X(b) - F_X(a)$