A standard six-sided die is thrown. Calculate the mean and variance of the number shown.

The die is thrown $n$ times. By using Chebyshev's inequality, find an $n$ such that

$$\mathbb{P}\left(\left|\frac{Y_{n}}{n}-3.5\right|>1.5\right) \leqslant 0.1$$

where $Y_{n}$ is the total of the numbers shown over the $n$ throws.