Question

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

Answer 1

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:

`alpha/2 = 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.