Are the probabilities in normal distribution tables given typically to the right or left of the $Z$ score?
One such text I am reading says to the right.
However, in my lecturer's exercises, I encountered a problem asking:
If $X \sim N(1,2) $ find $P(X>0)$.
Since $Z \sim \frac{X-\mu}{\sigma}$ then we have
$P(X>0) = P(\frac{X-1}{\sqrt{2}} > \frac{-1}{\sqrt{2}}) = P(Z > \frac{-1}{\sqrt{2}})$
= $1 - \Phi(-\frac{1}{\sqrt{2}})$
Now, if it's to the right, and we want to find $P(Z > \frac{-1}{\sqrt{2}})$
Don't we just need to look up $-\frac{1}{\sqrt{2}}$ in our table? Why would we minus it by one? The table gives us the values to the right of $\frac{-1}{\sqrt{2}}$ already.