How do i determine if standard deviation is known or unknown?

In fact, both questions require the use of the $t$-distribution critical value for $\nu = n-1 = 99$ degrees of freedom, namely $$t_{99,0.005} \approx 2.62641.$$

The reason for this is because the standard deviation provided in the problem, $3900$, is clearly stated to have been obtained from the sample of $n = 100$ automobile owners. Therefore, it is an estimate of the true parameter $\sigma$. The approximate $99\%$ confidence interval is then $$23500 \pm t_{99,0.005} \frac{3900}{\sqrt{100}} \approx [22475.7, 24524.3].$$

What aspect(s) of this interval estimate are approximate and what are the underlying assumptions?

• It is assumed that the annual mileage of a randomly chosen driver in Virginia is an approximately normally distributed random variable.
• It is assumed that the mileage of any driver is independent of the mileage of any other drivers.
• This interval estimate is only an approximation to the extent that the above assumptions are not met.

It would be inconsistent to apply the $z$-score critical value $z_{0.005}$ to the interval estimate, and then in the subsequent part of the question, apply the $t$-score.