Find the $z$ score for each student and indicate which one has the higher relative score.
$\begin{array}{|l|l|l|l|}
\hline \text { Art Major } & X=46 & \bar{X}=50 & s=5 \
\hline \text { Theatre Major } & X=70 & \bar{X}=75 & s=7 \
\hline
\end{array}$

A) The art major has a higher score than the theatre major.
B) The theatre major has a higher score than the art major.
C) Both students have the same score.
D) Neither student received a positive score; therefore, the higher score cannot be determined.

Question

Find the $z$ score for each student and indicate which one has the higher relative score. 
$\begin{array}{|l|l|l|l|}
\hline \text { Art Major } & X=46 & \bar{X}=50 & s=5 \
\hline \text { Theatre Major } & X=70 & \bar{X}=75 & s=7 \
\hline
\end{array}$

A) The art major has a higher score than the theatre major.
B) The theatre major has a higher score than the art major.
C) Both students have the same score.
D) Neither student received a positive score; therefore, the higher score cannot be determined.

Quizplus · Accepted Answer

We need to find the z-score for each student.

For the art major: 
$$z = \frac{X-\bar{X}}{s} = \frac{46-50}{5} = -0.8$$

For the theatre major: 
$$z = \frac{X-\bar{X}}{s} = \frac{70-75}{7} = -0.71$$

Since both z-scores are negative, we know that both students scored below the mean for their respective majors. However, the theatre major's z-score is slightly higher, indicating that they scored relatively better compared to their classmates than the art major did. Therefore, the theatre major has the higher relative score.

Find The zzz Score for Each Student and Indicate Which One Has the One

Find The $z$ Score for Each Student and Indicate Which One Has the One