probability of a standard normal distribution

Question

I haven't been able to make the sense of the following expression and use the table for standard normal distribution.

z_.10

Answer 1

Since the standard normal is symmetric about $0$, and by definition $\Pr(Z\le z_{0.1})=0.10$, it follows that $z_{0.1}$ must be negative.

Note also that by symmetry, for any $a$ we have $\Pr(Z\le -a)=\Pr(Z\ge a)$.

For what $a$ do we have $\Pr(Z\ge a)=0.10$? The right tail must have area $0.10$, so we must have $\Pr(Z\le a)=0.90$.

Now I expect you can use your table. Look in the body of the table until you see a number close to $0.9$. You should get something like $1.28$.

So $a\approx 1.28$, and therefore $-a$, our answer, is $\approx -1.28$.