Chapter 5.8, Problem 3E

Let X denote the outcome when a fair die is rolled. Then $\mu =\frac{7}{2}$ and ${\sigma }^2=\frac{35}{12}$.

Note that the maximum deviation of X from $\mu$ equals $\frac{5}{2}$.

Express this deviation in terms of the number of standard deviations: that is, find k, where $k\sigma =\frac{5}{2}$.

Determine a lower bound for $P\left(\left|X-3.5\right|<2.5\right)$.