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?

a. the z score of 0 is most preferable because it corresponds to a test score equal to the mean.
b. the z score of - 1.00 is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score.
c. the z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.
d. the z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score.
e. the z score of - 2.00 is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores.

Explanation:

The z - score represents the number of standard deviations a data - point is from the mean. A higher z - score means the data - point is further above the mean. Among the given z - scores (-2.00, - 1.00, 0, 1.00, 2.00), 2.00 is the highest, indicating a score that is 2 standard deviations above the mean, which corresponds to the highest of the possible scores among the given options.

Answer:

C. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.