I have the following question:
The heights of a random sample of $50$ college students showed a mean of $174.5$ centimeters and a standard deviation of $6.9$ centimeters.
Construct a $98%$ confidence interval for the mean height of all college students.
While learning about estimating the population mean using the sample mean I learned about $2$ cases:
$1.$ The population standard deviation $\sigma$ is known: we use the Z distribution (standard normal) to estimate it
$2.$ The population standard deviation $\sigma$ is unknown, we use the T-distribution, under the condition that around population is normally or approximately normally distributed
However, this question doesn't fall under either of these as $\sigma$ is unknown and we do have any info about the distribution of the population, the author solved it using the Z distribution and just took the population standard deviation to be $6.9$
My question: Is this a common practice to do (taking the sample sd to be the same as the population sd when we don't have it)? Are there any conditions to do this? Or did I just misunderstabdd something?