Determine which score corresponds to the higher relative position.
-Which score has the highest relative position: a score of 36 on a test for which $x = 26$ and $s = 10$, a score of $5.6$ on a test for which $\bar { x } = 4.6$ and $s = 0.8$ or a score of 468 on a test for which $\bar { x } = 413$ and $s = 50$ ?
A) A score of 36
B) A score of 468
C) A score of $5.6$

Question

Quizplus · Accepted Answer

To determine the relative position of each score, we calculate the z-score for each, using the formula $z = \frac{(X - \bar{X})}{s}$, where $X$ is the score, $\bar{X}$ is the mean, and $s$ is the standard deviation. For the first score: $z = \frac{(36 - 26)}{10} = 1$For the second score: $z = \frac{(5.6 - 4.6)}{0.8} = 1.25$For the third score: $z = \frac{(468 - 413)}{50} = 1.1$The score of 5.6 has the highest z-score (1.25), indicating it has the highest relative position among the given scores.

Determine Which Score Corresponds to the Higher Relative Position x=26x = 26x=26

Determine Which Score Corresponds to the Higher Relative Position $x = 26$