A population exits that follows a normal distribution with a mean of 15 and a standard deviation of 3. If we randomly sample 25 items and find the sample mean to be 14, what is the Z score corresponding to this value?

Answer:

Given:

The Population Mean $ (μ)=15 $

The Population Standard Deviation $ (σ)=3 $

The Sample Size $ (n)=25 $

Solution:
The z-score for a sample mean:
$z = (x\bar-\mu)/(\sigma/\sqrt(n))= (14-15)/(3/\sqrt(25)) = -1.667$

Final answer:
The z-score for a sample mean $(z) = -1.667 $