Question

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

Answer 1

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:

`alpha/2 = 0.05/2 = 0.025`

which we can use our table to find `-z` where `Phi(-z) = 0.025`
thus `-z = -1.96` and `z = 1.96`

this is easier understood with images.