For admission to graduate school, Ivan is taking the biology subject-matter test, and Goran is taking the physics subject-matter test. Ivan scored 531 on the biology test, and Goran scored 653 on the physics test. For each of these subject-matter tests, the distribution of scores is bell-shaped. Scores for the biology test have a population mean of 625 points with a standard deviation of 29 points. Scores for the physics test have a population mean of 566 points with a standard deviation of 41 points.

(a) Find the z-scores of Ivan's performance as a score on the biology test and Goran's performance as a score on the physics test. Round your answers to two decimal places.

- z-score of Ivan's score:
- z-score of Goran's score:

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

- Ivan
- Goran
- It is unclear who scored higher relative to his population.

Question

High School

Answer :

jaiswaljyoti jaiswaljyoti · Answer 1 · 2023-08-05T19:58:08-04:00

Goran scored higher relative to his population.

To find the z-scores of Ivan's performance on the biology test and Goran's performance on the physics test, we will use the formula:

z = (x - μ) / σ

For Ivan's biology test score:

z = (531 - 625) / 29 = -3.24

For Goran's physics test score:

z = (653 - 566) / 41 = 2.12

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

Ivan's z-score is -3.24, which means his score is 3.24 standard deviations below the mean of the biology test scores.

Goran's z-score is 2.12, which means his score is 2.12 standard deviations above the mean of the physics test scores.

Since a higher z-score indicates a higher score relative to the population, Goran scored higher relative to his population.

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

https://brainly.com/question/33144694

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