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

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May 18, 2015

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.

enter image source here

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