I assume that you're talking about a
standard normal distribution. if you have a two tailed test with confidence interval of 95%, your \(\displaystyle \alpha\)/2= 0.025. The zero is in the center of the distribution.
What matters is the area underneath the curve. The full area under the curve is always 1. So, a 95% interval is 95% of 1, or 0.95.
The x axis is actually a Z axis. giving values of Z from the equation
\(\displaystyle z=\frac{\bar{x}-\mu}{\sigma}\)
So, a Z value of zero just means that your sample mean (\(\displaystyle \bar{x}\)) and actual mean (\(\displaystyle \mu\)) are equal.
A 95% confidence interval means that you have half the area of 0.95 on the positive side of zero and the same on the negative side. So, if you look up 0.475 in a
Z table, you will get a value of 1.96. Similarly, you will get a Z value of -1.96 in the negative direction.
Let me know if you have any other specific questions. I'm not sure what exactly you need to know.
