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To find the cut off 37% from the bottom of z scores.
The z scores are the standard normal variates with a normal distribution.
So we have probabilty of z is <= x such that this probability is 37%.
Therefore P(z < = x) = 37%.
We know that Z has the standard normal distribution. So P(z<=0) = 0.5.
Therefore p(z > -x) = 0.37 = , as normal distribution is sy mmetrical.
Therefore P(0 <= z< - x) = 0.5+(0.5-37) = 1-.37 = 0.63.
From normal probablity tables , -x = 0.332. Or x = -0.332.
Therefore , the below cut off 37% of the z scores is at z = -0.332 , or at z = -0.33 (rounded of to 2 decimals ).
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