Find the z value such that 90% of the area under the standard normal curve lies between z and z.

Question

The answer is $\frac{1-.9000}{2}$ but why is that? Why do we not multiply by 2 and instead divide by two?

There are two z values so $1=0.9000$ $=$ the negative z value so why not multiply by two for the other z value?

Answer 1

You need to divide by 2 because the distribution has two tails; one is the part of the distribution above $z$, and the other is the part of the distribution below $-z$. So, only $0.10/2$ of the area is beyond $z$.