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For admission to graduate school, Maria is taking the English subject-matter test, and Maya is taking the mathematics subject-matter test. For each of these tests, the distribution of scores is clearly bell-shaped.

Scores for the English test have a population mean of 591 points with a standard deviation of 45 points. Scores for the mathematics test have a population mean of 641 points with a standard deviation of 28 points. Maria scored 714 on the English test, and Maya scored 701 on the mathematics test.

(a) Find the z-scores of Maria's performance on the English test and Maya's performance on the mathematics test. Round your answers to two decimal places.

- z-score of Maria's score:
- z-score of Maya's score:

(b) Relative to her population, who scored lower? Choose the best answer based on the z-scores of the two test scores.

- Maria
- Maya
- It is unclear who scored lower relative to her population.

Answer :

Final answer:

Maria's z-score on the English test is 2.73, while Maya's z-score on the mathematics test is 2.14. This means Maria scored higher above the mean of her test than Maya did, so relative to their respective populations, Maya scored lower.

Explanation:

To find the z-scores of Maria and Maya, we use the formula for the z-score, which is (x-μ)/σ, where x is the individual score, μ is the mean score, and σ is the standard deviation.

Let's first calculate Maria's z-score. Maria scored 714 on the English test while the mean score is 591 with a standard deviation of 45. Her z-score would thus be (714-591)/45, which equals 2.73 (rounded to two decimal places).

Maya, on the other hand, scored 701 on the mathematics test, with a mean score of 641 and a standard deviation of 28. Her z-score would be (701-641)/28, equalling 2.14 (rounded to two decimal places).

In response to the second part of the question (b), who scored lower relative to her population, the z-score helps us understand how a particular score compares to the population mean, in terms of standard deviations.

A higher z-score implies that a score is further above the mean. Therefore, since Maria has a higher z-score, it means her score is further above the mean than Maya's score. Thus, relative to her population, Maya scored lower.

Learn more about z-scores here:

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