| $X _ { i }$ | 0 | 1 | 2 | 3 | 4 | 5 |
| $f _ { i }$ | $k + 2$ | $2k$ | $k ^ { 2 } - 1$ | $k ^ { 2 } - 1$ | $k ^ { 2 } + 1$ | $k - 3$ |
Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution
\begin{center}
\begin{tabular}{ c l l c c l l }
$X _ { i }$ & 0 & 1 & 2 & 3 & 4 & 5 \\
$f _ { i }$ & $k + 2$ & $2k$ & $k ^ { 2 } - 1$ & $k ^ { 2 } - 1$ & $k ^ { 2 } + 1$ & $k - 3$ \\
\end{tabular}
\end{center}
where $\Sigma f _ { i } = 62$. If $\lfloor x \rfloor$ denotes the greatest integer $\leq x$, then $\lfloor \mu ^ { 2 } + \sigma ^ { 2 } \rfloor$ is equal to\\
(1) 9\\
(2) 8\\
(3) 7\\
(4) 6