It is good that you are paying attention to details in @Dave's nice Answers (+1). But the experimental situation you describe is an easy one. You anticipate having plenty of data and it is hard to imagine that your answer
needs to have extraordinary precision.
The population parameter $\mu$ is the mean height in your student population.
The only way for you to know its exact value is to measure all the students, which you say (quite reasonably) you cannot do.
Data. Suppose you get data to the nearest cm. that are summarized as shown below.
[I am using R statistical software, but other software gives similar summaries.]
summary(x); sd(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
151.0 168.0 175.0 174.7 181.0 205.0
[1] 9.083249
The sample mean $\bar X = \frac 1{500} \sum_{i=1}^{500} X_i = 174.7$ cm
and the sample standard deviation $S_x = \sqrt{\frac {1}{499}\sum_{i=1}^{500}(X_i - \bar X)^2} = 9.083.$ With $n = 500$ subjects, we expect the population mean to be $\mu \approx 175$ and the population standard deviation to be
$\sigma \approx 9.$ These are first impressions, to be refined presently.
A histogram of the data is shown below.

Assumption of normality. In past experience, people's heights have usually been approximately normally
distributed. Also, the fact the the sample mean 174.7 and median 175 are nearly equal and the general shape of the histogram indicate that the data are at least roughly normally distributed.
If you are really worried whether you data are nearly normal, you could do
a formal test. For the data shown above, a Shapiro-Wilk test of normality gives
the P-value 0.146. A P-value below 0.05 would indicate that the data are not from a normal population.
shapiro.test(x)$p.val
[1] 0.1461765
Also, the t confidence interval described below is known to perform well even if the data are not perfectly normal. The Central Limit Theorem guarantees
that samples as large as $n = 500$ can depart a bit from normality and still give very useful results.
Confidence interval. In order to get an idea how far our estimate $\bar X = 174.7$ might be from the unknown population mean $\mu,$ we can make a 95% confidence interval (CI) of the form
$\bar X \pm 1.965 S/\sqrt{n},$ where the numbers $\pm 1.965$ cut off probability 0.025 from the upper and lower tails of Student's t distribution with $n - 1 = 499$ degrees of freedom (which leaves 95% of the probability between these two numbers). For samples as large as $n=500$ this number is roughly $2$ and some people just use 2 when making a 95% confidence interval.
qt(.975, 499)
[1] 1.964729
The procedure t.test
in R, makes a 95% confidence interval. (Most other
statistical software packages have procedure that do the same.) The resulting
95% CI is $(173.9, 175.5).$
t.test(x)$conf.int
[1] 173.9419 175.5381
attr(,"conf.level")
[1] 0.95
At this point, it is OK to round to one decimal place because we usually aren't
interested in expressing people's heights more precisely than one mm.
We conclude it is likely that the population mean height $\mu$ is between 173.9 and 175.5. There is a small chance that $\mu$ may be a little bit outside this
interval, but for practical purposes it seems good enough to say that
$\mu \approx 174.7$ or $175$ cm.--with a margin of error around $8$ mm.
If you wanted to have more than 95% confidence in your interval, you could make a 99% confidence interval $(173.7, 175.8)$, which is a little longer (with a margin of error about $1$ cm).
t.test(x, conf.lev=.99)$conf.int
[1] 173.6896 175.7904
attr(,"conf.level")
[1] 0.99
Note: In order to determine whether student's heights decrease between morning and evening, a very careful study was done in India in the mid-1940s.
Students were measured as accurately as possible in the AM and PM by two different people. Results were analyzed to make sure the two technicians made
consistent height measurements. They tried (almost successfully) to measure
student heights to the nearest mm.
They concluded that overall most students
lose about a cm in height between morning and evening (gaining it back after
a night's sleep).
If you are doing your own study of student heights, you
may be interested in details of their work and analysis, reported by Majumbar DN and Rao CR (1958) "Bengal anthropometric survey, 1945," Sankhya, V.19, Parts 3 & 4.