Comparison of Z-Scores for Students

Very Hard Data Analysis Interpretation Of Data

Consider a dataset representing the scores of students in a mathematics test. The mean (ar{x}) score of the dataset is 82, with a standard deviation (s) of 10. Additionally, the scores are believed to follow a normal distribution. The score of Student A is 88, while the score of Student B is 74.

To analyze how these scores compare to the overall performance in the test, we will calculate the z-scores for both Student A and Student B using the formula:

$$ z = rac{x - ar{x}}{s} $$

Where:

$x$ is the raw score
$$ar{x}$$ is the mean score
$$s$$ is the standard deviation

After finding the z-scores, evaluate the statements below:

Quantity A is greater than Quantity B.

Quantity A is less than Quantity B.

Quantity A is equal to Quantity B.

The relationship cannot be determined from the information given.

Hint

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