Anna goes to a school in Italy, which uses a 10 point grade scale, while Bill’s school in the USA uses a 4 point grade scale. They report their standardized z-scores for their GPAs as z(ann) = -0.42 and z(bill) = -2.20. Which student has the more UNUSUAL grade point average relative to their own classmates?
A. Their z-scores are too close to make a determination.
B. Anna, because her z-score is further from the mean than Bill’s.
C. Bill, because his z-score is further from the mean than Anna’s.
D. Anna, because her z-score is greater than Bill’s.
E. Bill, because his z-score is greater than Anna’s.
Explain your thinking.
The mean score will always be a z score of 0
Lower than the mean will have negative z scores and higher will have positive z scores.
99.7% of all the scores will have z scores of between -3 and +3.
Both Ann and Bill did badly because their z score is negative (less than 0)
The one that is more unusual will be the one whose score is furthest from 0.
In this case that worst one. Which one is that?
Let's see if I can finish this problem. The z-score for Anna is -0.42 and the z-score for Bill is -2.20. They both have a z-score less than 0, but the one that has the more UNUSUAL grade point average is Bill with a z-score furthest from 0. The answer will be C. Bill, because his z-score is further from the mean than Anna’s. Thank you for helping!