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

May 17, 2015

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 $- z = - 0.15$