Given 10 nail lengths with
$$\bar{x} = 59.98 \quad,\quad\sigma = 0.26$$
Q: What is the shortest average nail length on basis of the sample probe? You can freely choose the level of significance.
I guess they want the lower bound of the confidence intervall.
I found out that the lower bound is described as
$$\bar{x}-z\cdot\frac{\sigma}{\sqrt{n}}$$
Lets say $\alpha = 5\%$
How do I calculate the z-score without having a $\mu$?