Salaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $6,300. We randomly survey ten teachers from that district.Please label each part ### Exercise Solutions with Explanations#### Part (d)**Problem**: Give the distribution of ΣX. (Round your answers to two decimal places.)**Solution Format**: ΣX ~ N(Mean, Standard Deviation)- **Entered Solution**: ΣX ~ N(41,000, 6300)- **Explanation**: This indicates that the sum of variable X follows a normal distribution with a mean of 41,000 and a standard deviation of 6,300.#### Part (e)**Problem**: Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.)- **Entered Solution**: 0- **Explanation**: The probability of earning over $400,000 is calculated to be 0, indicating an error in calculation or understanding.#### Part (f)**Problem**: Find the 80th percentile for an individual teacher’s salary. (Round your answer to the nearest whole number.)- **Entered Solution**: $3600- **Explanation**: The 80th percentile is incorrectly calculated, suggesting a misunderstanding of percentile computation.#### Part (g)**Problem**: Find the 80th percentile for the sum of ten teachers' salary. (Round your answer to the nearest whole number.)- **Entered Solution**: $44,060- **Explanation**: This solution was also incorrect, indicating errors in determining the sum's percentile.#### Part (h)**Problem**: If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part (d)?- **Correct Choice**: The distribution would be a more symmetrical normal curve.- **Explanation**: Surveying more teachers would result in a sample distribution that is closer to a normal distribution due to the Central Limit Theorem.#### Part (i)**Problem**: If each of the 70 teachers received a $3000 raise, graphically, how would that change the distribution in part (b)?- **Correct Choice**: The distribution would shift to the right.- **Explanation**: A $3000 raise across the board would translate to a shift to the right in the distribution, reflecting the increase in salaries.### Diagrams or Graphs ExplanationThere aren't any graphs or diagrams present in the provided image. The problems involve conceptual understanding of statistical distribution and graphical interpretation based on hypothetical changes in

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Description: Salaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $6,300. We randomly survey ten teachers from that district.Please label each part ### Exercise Solutions with

(d) Determine the distribution of Σx. The distribution of Σx is determined below as follows:

Answered: Salaries for teachers in a particular…

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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Salaries for teachers in a particular elementary school district are normally distributed with a mean of $41,000 and a standard deviation of $6,300. We randomly survey ten teachers from that district.

Please label each part

### Exercise Solutions with Explanations

#### Part (d)
**Problem**: Give the distribution of ΣX. (Round your answers to two decimal places.)

**Solution Format**: ΣX ~ N(Mean, Standard Deviation)

- **Entered Solution**: ΣX ~ N(41,000, 6300)
- **Explanation**: This indicates that the sum of variable X follows a normal distribution with a mean of 41,000 and a standard deviation of 6,300.

#### Part (e)
**Problem**: Find the probability that the teachers earn a total of over $400,000. (Round your answer to four decimal places.)

- **Entered Solution**: 0
- **Explanation**: The probability of earning over $400,000 is calculated to be 0, indicating an error in calculation or understanding.

#### Part (f)
**Problem**: Find the 80th percentile for an individual teacher’s salary. (Round your answer to the nearest whole number.)

- **Entered Solution**: $3600
- **Explanation**: The 80th percentile is incorrectly calculated, suggesting a misunderstanding of percentile computation.

#### Part (g)
**Problem**: Find the 80th percentile for the sum of ten teachers' salary. (Round your answer to the nearest whole number.)

- **Entered Solution**: $44,060
- **Explanation**: This solution was also incorrect, indicating errors in determining the sum's percentile.

#### Part (h)
**Problem**: If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part (d)?

- **Correct Choice**: The distribution would be a more symmetrical normal curve.
- **Explanation**: Surveying more teachers would result in a sample distribution that is closer to a normal distribution due to the Central Limit Theorem.

#### Part (i)
**Problem**: If each of the 70 teachers received a $3000 raise, graphically, how would that change the distribution in part (b)?

- **Correct Choice**: The distribution would shift to the right.
- **Explanation**: A $3000 raise across the board would translate to a shift to the right in the distribution, reflecting the increase in salaries.

### Diagrams or Graphs Explanation
There aren't any graphs or diagrams present in the provided image. The problems involve conceptual understanding of statistical distribution and graphical interpretation based on hypothetical changes in

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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