# How do you find the z-score for which 76% of the distribution's area lies between -z and z?

May 18, 2015

Firstly in this question, we need to solve for $\alpha$ which is the part of the distribution of which we not looking for.

we can do this with the sum:
$\alpha = 1 - 0.76 = 0.24$

as 0.76 = 76%

we also know that our Standard Normal Distribution is symmetric, so we must divide that $\alpha$ to be split on either side of our distribution. so we solve for:

$\frac{\alpha}{2} = \frac{0.24}{2} = 0.12$

then we find a correlating $z$-score for the value $0.12$

and we get that $- z = - 1.175$ and $z = 1.175$

This becomes easier to understand when visualized, so observe how we do this sum.