Question

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: 2.00, 1.00, 0, 1.00, 2.00? Why?

1) 2.00
2) 1.00
3) 0
4) 1.00
5) 2.00

Answer 1

You would prefer the highest positive z-score, which is 2.00, as it indicates that your score is two standard deviations above the mean, corresponding to a higher performance relative to classmates.

Step-by-step explanation:

If your score on the next statistics test is converted to a z-score, you would prefer the highest positive z-score, which in the given options is 2.00. A z-score represents the number of standard deviations a score falls above (positive z-score) or below (negative z-score) the mean of the distribution. Thus, if Susan's z-score was 2.0, it means she scored two standard deviations above the class mean for the exam. A z-score of 2 typically correlates with a higher percentile rank relative to the class, indicating a better performance in comparison to classmates. In the context of the standard normal distribution (Z ~ N(0, 1)), a z-score of 2 would place a student approximately in the 97th percentile, meaning they performed better than about 97% of the class.