For admission to graduate school, Latoya is taking the English subject-matter test, and Salma is taking the German subject-matter test. Latoya scored 580 on the English test, and Salma scored 495 on the German test. For each of these subject-matter tests, the distribution of scores is clearly bell-shaped. Scores for the English test have a population mean of 639 points with a standard deviation of 22 points. Scores for the German test have a population mean of 533 points with a standard deviation of 18 points.

(a) Find the z-scores of Latoya's performance as a score on the English test and Salma's performance as a score on the German test. Round your answers to two decimal places.

- Z-score of Latoya's score:
- Z-score of Salma's score:

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

A. Latoya
B. Salma
C. It is unclear who scored lower relative to her population.

Question

High School

Answer :

suchitakm42 suchitakm42 · Answer 1 · 2024-09-03T18:02:08-04:00

Salma scored lower relative to her population.

To find the z-scores of Latoya's performance on the English test and Salma's performance on the German test, we will use the formula:

z = (x - μ) / σ

where z is the z-score, x is the data point, μ is the population mean, and σ is the standard deviation.

For Latoya's score on the English test:

z = (580 - 639) / 22 = -2.68

For Salma's score on the German test:

z = (495 - 533) / 18 = -2.11

Now, let's compare the z-scores to determine who scored lower relative to their population:

Latoya's z-score is -2.68, which means her score is 2.68 standard deviations below the mean of the English test scores.

Salma's z-score is -2.11, which means her score is 2.11 standard deviations below the mean of the German test scores.

Since a lower z-score indicates a lower score relative to the population, we can conclude that Salma scored lower relative to her population.

Learn more about calculating z-scores and comparing test scores here:

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