Cutoffs:Find the corresponding Z score(s). Round answer to 2 decimal places! Cutoff for the bottom 37%.

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 ).