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.

Given : For geography test student score, x = 68.0 population mean, μ = 80.0 population standard deviation, σ= 10.0 For mathematics test student score, x = 282.0 population mean, μ = 300.0 population standard deviation, σ= 12.0solution : Z score for geography test = 68.0 - 80.0 / 10.0 = -1.2 and Z score for Mathematics test = 282.0 - 300.0 / 12.0 = -1.5Here Z score of geography test is greater than z score of mathematics test therefore Student scores better on geography test so, option c) is correct answer

Answered: The studernt scored the same on both…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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