MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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A student scores 68 on a geography test and 282 on a mathmatics test. Geography test had mean of 80 and standard deviation of 10. Math test had mean of 300 and standard deviation of 12. If the data for both tests both are normally distributed, on which test did the student score better relative to the other students in each class?
A student scores 68 on a geography test and 282 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 10. The mathematics test has a mean of 300 and a standard deviation of 12. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class?

- **A.** The student scored the same on both tests.
- **B.** The student scored better on the mathematics test.
- **C.** The student scored better on the geography test.

**Explanation:**

To determine which test the student performed better on relative to peers, we can calculate the z-scores for each test.

1. **Geography Test:**
   - Score = 68
   - Mean = 80
   - Standard deviation = 10
   - Z-score = \((68 - 80) / 10 = -1.2\)

2. **Mathematics Test:**
   - Score = 282
   - Mean = 300
   - Standard deviation = 12
   - Z-score = \((282 - 300) / 12 = -1.5\)

The student has a higher (less negative) z-score for the geography test, indicating they performed relatively better on that test compared to the mathematics test. Therefore, the correct choice is **C.** The student scored better on the geography test.
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Transcribed Image Text:A student scores 68 on a geography test and 282 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 10. The mathematics test has a mean of 300 and a standard deviation of 12. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class? - **A.** The student scored the same on both tests. - **B.** The student scored better on the mathematics test. - **C.** The student scored better on the geography test. **Explanation:** To determine which test the student performed better on relative to peers, we can calculate the z-scores for each test. 1. **Geography Test:** - Score = 68 - Mean = 80 - Standard deviation = 10 - Z-score = \((68 - 80) / 10 = -1.2\) 2. **Mathematics Test:** - Score = 282 - Mean = 300 - Standard deviation = 12 - Z-score = \((282 - 300) / 12 = -1.5\) The student has a higher (less negative) z-score for the geography test, indicating they performed relatively better on that test compared to the mathematics test. Therefore, the correct choice is **C.** The student scored better on the geography test.
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