Kate received a z score of 1 on a reading test.What do we know about Kate's performance,assuming that the reading test scores are distributed normally?
A) She scored better than 84% of other students.
B) She scored better than only 2/3 of the other students.
C) She scored worse than only 2/3 of other students.
D) She scored worse than 84% of other students.

Question

Quizplus · Accepted Answer

A z-score of 1 means that Kate's score is one standard deviation above the mean. Using the empirical rule, we know that approximately 68% of scores fall within one standard deviation of the mean, and since we are dealing with a normal distribution, we can assume symmetry around the mean. Therefore, Kate's score is better than 50% of the other students who took the test, plus an additional 34% (half of the remaining 68%) who fall between one and two standard deviations above the mean. This gives a total of 84%.

Kate Received a Z Score of 1 on a Reading