= Solution
Use the quoted event with, for example, $\alpha=1/4$, so at least $3k/4$ clean block means obey the uniform bound. Replacing at most $\epsilon n$ observations can corrupt at most $\epsilon n$ blocks. If $k\geq4\max\{n\epsilon,1\}$, at least $3k/4-\epsilon n\geq k/2$ block means remain both uncorrupted and good; adjusting constants handles equality and integer rounding. Their strict majority forces every projected median to obey the same uniform bound. Applying part b and absorbing fixed constants gives
$$
\|\widehat\mu(Z)-\mu_0\|_2
\leq c''\sqrt{
\frac{\max\{\operatorname{tr}(\Sigma),\|\Sigma\|_2k\}}n}
$$
with probability at least $1-e^{-c'k}$.
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