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# How do you find the z-score for which 95% of the distribution's area lies between -z and z?

May 19, 2015

for this question, we would first need to find $\alpha$ the area underneath the cure which does not lay between $- z$ and $z$

alpha = 100% - 95% = 1 - 0.95 = 0.05

now we also know that our Standard Normal Distribution is symmetrical, so we divide $\alpha$ to equally be on either side of our wanted area.

so we get:

$\frac{\alpha}{2} = \frac{0.05}{2} = 0.025$

which we can use our table to find $- z$ where $\Phi \left(- z\right) = 0.025$
thus $- z = - 1.96$ and $z = 1.96$

this is easier understood with images.