What z score values represents the middle 90% of the values in a normal distribution?
Solution:
Middle 90% of the value in a normal distribution
Middle grey area = 90% =0.90
Left white area= 5%=0.05
Right white area= 5%=0.05
We know that
"Z_{0.0505}=-1.64\\\\\n\\text{and}\\\\\nZ_{0.0495}=-1.65\\\\\n\n\\text{then \\space average} \n\\\\\nZ_{0.05 \\space left}=-1.645\\\\\n\n\\text{so}\\\\\nZ_{0.05 \\space right}=+1.645\\\\"
So we get, z- score value represents the middle 90% of the value in a normal distribution
-1.645 to +1.645
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