Question

What z score values represents the middle 90% of the values in a normal distribution?

Answer 1

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

$Z_{0.0505}=-1.64\\ \text{and}\\ Z_{0.0495}=-1.65\\ \text{then \space average} \\ Z_{0.05 \space left}=-1.645\\ \text{so}\\ Z_{0.05 \space right}=+1.645\\$

So we get, z- score value represents the middle 90% of the value in a normal distribution

-1.645 to +1.645