= Solution
{c}
At <sample size> 100, keep essentially the same numerical <confidence interval>, but treat its calibration as approximate. For independent heights with finite, nonzero <variance>, the <central limit theorem> makes the <sample mean> approximately <normally distributed>, and the <sample variance> consistently estimates the population <variance>. Hence the <studentized sample mean> is approximately standard normal even without a <normal distribution> for individual heights.
Using the permitted cutoff 2 gives
$$
\boxed{\mu\approx\overline x\pm2\frac{s}{\sqrt n}
=[170.0,173.4]\ \mathrm{cm}\quad\text{at approximately 95\% confidence}.}
$$
A <Student t-distribution> cutoff gives a similar approximation for large <sample size>, but its justification at fixed <sample size> is no longer exact. Extreme skewness or influential <outliers> could make 100 observations insufficient for accurate <coverage probability>; abandoning <normality> alone supplies no specific numerical correction. The <sampling with replacement> assumption still precludes a <finite population correction>.
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