Question

a score most farthest to the mean (most extreme) would be indicated by which z - score?
-0.50
-1.00
-3.00
+2.00

Explanation:

Step1: Understand z - score concept

The z - score represents the number of standard deviations a data point is from the mean. The larger the absolute value of the z - score, the farther the data point is from the mean.

Step2: Calculate absolute values

Calculate the absolute value of each z - score:
For \(z=-0.50\), \(| - 0.50| = 0.50\);
For \(z = - 1.00\), \(| - 1.00|=1.00\);
For \(z=-3.00\), \(| - 3.00| = 3.00\);
For \(z = + 2.00\), \(|2.00|=2.00\).

Step3: Compare absolute values

Compare the absolute values: \(0.50<1.00<2.00<3.00\).

Answer:

-3.00