# How do you find the z-score for having area 0.07 to its right under the standard normal curve, that is, how do you find z0.07?

May 20, 2015

To solve for ${Z}_{\alpha}$ where $\alpha$ is the area to the right of the Standard Normal curve at point $Z$ ...

We know our table for $Z$ scores gives us area to the left, so what we do is "convert" the question, to have is ask for the area to the left.

So, we know that the total area under the curve is equal to $1$

Now we solve for $1 - \alpha$ which will give us the area to the left of our curve. which then becomes more simple to solve for $Z$.

Thus for ${Z}_{0.07}$ we have $\alpha = 0.07$, then we look for $1 - \alpha = 1 - 0.07 = 0.93$

So now we solve for $Z$ where $\Phi \left(Z\right) = 0.93$

we take a look at our table, and get the answer that $\Phi \left(1.474\right) = 0.93$

Therefore ${Z}_{0.07} = 1.475$.