Questions: A student in a statistics class took the midterm and was told by the professor that her z-score for the exam was 1.5. What does this tell us about the student's score relative to the rest of the class? Her score is 1.5 standard deviations below the mean Her score is 1.5 standard deviations above the mean Her score is 1.5 points below the mean Her score is 1.5 points above the mean Her score is 15% higher than the class mean Her score is 15% lower than the class mean

A student in a statistics class took the midterm and was told by the professor that her z-score for the exam was 1.5. What does this tell us about the student's score relative to the rest of the class?

Her score is 1.5 standard deviations below the mean

Her score is 1.5 standard deviations above the mean

Her score is 1.5 points below the mean

Her score is 1.5 points above the mean

Her score is 15% higher than the class mean

Her score is 15% lower than the class mean

Transcript text: A student in a statistics class took the midterm and was told by the professor that her 2-score for the exam was 1.5. What does this tell us about the student's score relative to the rest of the class? Her score is 1.5 standard deviations below the mean Her score is 1.5 standard deviations above the mean Her score is 1.5 points below the mean Her score is 1.5 points above the mean Her score is $15 \%$ higher than the class mean Her score is $\mathbf{1 5 \%}$ lower than the class mean

Solution

Solution Steps

Step 1: Understanding the Z-Score

The student's z-score is given as $ z = 1.5 $. The z-score indicates how many standard deviations a data point is from the mean of a distribution. A positive z-score means the score is above the mean.

Step 2: Interpretation of the Z-Score

Since $ z = 1.5 $, we can conclude that the student's score is $ 1.5 $ standard deviations above the mean. This can be mathematically expressed as: \[ \text{Score} = \mu + 1.5\sigma \] where $ \mu $ is the mean score of the class and $ \sigma $ is the standard deviation.