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

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May 19, 2015

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.

enter image source here

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