assuming that you wished to have the highest possible score on an exam relative to ht e other scores, would you rather have a score of 70 on a test with a mean of 60 and a standard deviations of 5.2 or a score of 81 on a test with a mean of 79 and a standard deviation of 7.1?
Find the z-score of each.
The one with the higher z-score is a "better score"
To determine which score will yield a higher relative score, we need to compare the scores by their respective positions in the distribution using z-scores. The z-score formula is (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.
Let's calculate the z-score for the score of 70 on the first test:
z1 = (70 - 60) / 5.2
z1 = 1.923
Now, let's calculate the z-score for the score of 81 on the second test:
z2 = (81 - 79) / 7.1
z2 = 0.282
The z-scores help us determine how many standard deviations a score is above or below the mean. In this case, a positive z1 value indicates that the score of 70 is above the mean, and a positive z2 value indicates that the score of 81 is also above the mean.
Since the z1 value (1.923) is larger than the z2 value (0.282), it suggests that the score of 70 on the first test is relatively higher than the score of 81 on the second test when compared to their respective distributions.
Therefore, if your goal is to have the highest possible score relative to the other scores, you would choose a score of 70 on the test with a mean of 60 and a standard deviation of 5.2.