Questions: Clarice was in the process of creating a report on the performance of her students and was trying to determine the z-score related to overall student scores. the mean percentage of students was 75% and the standard deviation was 10%, what z-score would correspond to a student that ended the course with an 85%? -2 -1 1 2 -3

Clarice was in the process of creating a report on the performance of her students and was trying to determine the z-score related to overall student scores. the mean percentage of students was 75% and the standard deviation was 10%, what z-score would correspond to a student that ended the course with an 85%? -2 -1 1 2 -3
Transcript text: Clarice was in the process of creating a report on the performance of her students and was trying to determine the z-score related to overall student scores. the mean percentage of students was $75 \%$ and the standard deviation was $10 \%$, what z-score would correspond to a student that ended the course with an 85\%? $-2$ $-1$ 1 2 $-3$
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Solution

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Solution Steps

Step 1: Given Information

We are provided with the following information:

  • Mean percentage of students, \( \mu = 75 \)
  • Standard deviation, \( \sigma = 10 \)
  • Student's score, \( X = 85 \)
Step 2: Z-Score Calculation

The z-score is calculated using the formula:

\[ z = \frac{X - \mu}{\sigma} \]

Substituting the known values:

\[ z = \frac{85 - 75}{10} = \frac{10}{10} = 1.0 \]

Step 3: Result Interpretation

The calculated z-score of \( 1.0 \) indicates that the student's score of \( 85\% \) is \( 1 \) standard deviation above the mean score of \( 75\% \).

Final Answer

The z-score corresponding to a student that ended the course with an \( 85\% \) is \\(\boxed{1.0}\\).

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