I'm doing a statistics course, and I thought I had no problems using distribution tables to find values. For example, for the Gauss distribution, if I want $\Phi(-2)$, I will do $1 - \Phi(2)$ because of symmetrical reasons.
We had one exercise where I have to find $z(0.1)$, and I was provided with the Gauss distribution table only. This may sound like a stupid question, but do I use this table to find $z(0.1)$? The mark scheme says that $z(0.1) = z(-0.9)$. I fail to comprehend this....from which side are they taking the distribution? Why is it $(-0.9)$? They end up with $z(0.1) = -1.28$. I don't know which table I'm supposed to use, I am only provided with the Gauss distribution table and I don't see any -1.28's anywhere... I don't understand the symmetry of this reasoning.
Thanks!
$z(0.1)$ means getting the $z$ value (argument of $\Phi$) for a given probability, in this case $0.1$. Since the table starts with probabilities of $0.5$, due to symmetry, you can retrieve the $z$ value by doing $-z(1-0.1)$. Then just look in the table where the highest probability $<0.9$ is. This is given for $\Phi(1.28)$. Thus, $z(0.1) = -1.28$.