The measurements of the times of a group of children competing in a race of The 100-m dash follows a normal distribution with a mean of 13.4 s and a standard deviation of 1.2 s. Among which values will be found the central 20% of runners?
Since we are given the 20% central, means the 20% of values around the mean, which also means the level of confidence is $p=0.2=1-\alpha\Rightarrow \alpha=0.8$, so $Z_{\alpha/2}=Z_{0.4}=0.255$ by looking at the table, hence the values will be the extreme values of the interval $[\mu-error, \mu+error]$, and $error=Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ but we don't have the $\sqrt{n}$, do we? Hence how else should I do this?