Question

How do you find the z score for which 12% of the distribution's area lies between z and -z?

Answer 1

Firstly we will find the area of which is not between `z` and `-z`

So we do the sum of `100% - 12% = 88%` which does not lie between `z` and `-z`

we know that our standard normal distribution is symmetric, so we would like to equally distribute the area that is not between `z` and `-z` on either side.

thus on each side of our area, we have `(88%)/2 = 44%`

and we will find in our table that `z=0.15` and `-z=-0.15`