Question

Imagine next week when you get your midterm back instead of seeing your score at the top you see a z score.
a. (2 point) What type of z-score would you want to see? Explain why.
b. (2 point) What would a positive z-score mean? Explain.

c. (2 point) What would a negative z-score mean? Explain. d. (2 point) What would a z-score of zero mean? Explain.

Answer 1

(a)

We want to see a high positive Z score, i.e., above + 3.0.

Reason: A high positive Z score, i.e., above + 3.0 indicates that my score is almost the maximum in the class: about 99.7% of the class are below my score.

(b)

A positive z-score means the actual score is above the mean of the whole class.

Explanation:
Z = (X - )/

So,

If Z > 0, it indicates: X>

(c)

(i)

A negative z-score means the actual score is below the mean of the whole class.

Explanation:
Z = (X - )/

So,

If Z < 0, it indicates: X<

(ii)

A z-score = 0 means the actual score is equal to the mean of the whole class.

Explanation:
Z = (X - )/

So,

If Z = 0, it indicates: X=