A woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard. The injury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a "normative" group of 27 similar cases and specified a reasonable award as one within two standard deviations of the mean of the awards in the 27 cases. The 27 awards were (in $1000s) 35, 63, 72, 113, 137, 142, 148, 151, 238, 290, 340, 410, 600, 750, 750, 754, 1050, 1100, 1135, 1150, 1200, 1200, 1250, 1577, 1700, 1825, and 2000, from which Ex, = 20,180, Ex² = 24,658,024. What is the maximum possible amount that could be awarded under the two-standard-deviation rule? (Round your answer to the nearest whole number.) LAUSE SALT thousand dollars
A woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard. The injury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a "normative" group of 27 similar cases and specified a reasonable award as one within two standard deviations of the mean of the awards in the 27 cases. The 27 awards were (in $1000s) 35, 63, 72, 113, 137, 142, 148, 151, 238, 290, 340, 410, 600, 750, 750, 754, 1050, 1100, 1135, 1150, 1200, 1200, 1250, 1577, 1700, 1825, and 2000, from which Ex, = 20,180, Ex² = 24,658,024. What is the maximum possible amount that could be awarded under the two-standard-deviation rule? (Round your answer to the nearest whole number.) LAUSE SALT thousand dollars
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![### Case Study: Determining Reasonable Compensation for Repetitive Stress Injuries
A woman sued a computer keyboard manufacturer, alleging that her repetitive stress injuries were caused by the keyboard. Initially, she was awarded about $3.5 million for pain and suffering. However, the court decided that this award was excessive and sought to establish a reasonable compensation by examining a "normative" group of 27 similar cases.
The court defined a reasonable award to be within two standard deviations of the mean of the awards in the 27 cases, which were as follows (in thousands of dollars):
\[35, 63, 72, 113, 137, 142, 148, 151, 238, 290, 340, 410, 600, 750, 750, 754, 1050, 1100, 1135, 1150, 1200, 1200, 1250, 1577, 1700, 1825, 2000\]
From these values, the sums were calculated as:
\[\sum x_i = 20,180\]
\[\sum x_i^2 = 24,658,024\]
#### Problem Statement:
What is the maximum possible amount that could be awarded under the two-standard-deviation rule? Round your answer to the nearest whole number and input your answer in thousands of dollars.
[Calculate Button]
#### Instructions:
1. **Understand the Dataset**: This data represents previous awards in similar cases. The court aims to identify a reasonable compensation by statistical measures.
2. **Calculate Mean and Standard Deviation**:
- **Mean**: Calculate the mean of the given awards.
- **Standard Deviation**: Compute the standard deviation to understand the spread of the data.
3. **Apply the Two-Standard-Deviation Rule**:
- Determine the range of awards that fall within two standard deviations of the mean.
4. **Find the Maximum Award**: Identify the highest award within this range, rounded to the nearest thousand dollars.
This exercise helps in understanding how courts can use statistical methods to determine reasonable compensation amounts in lawsuits involving financial awards.
### Key Concepts:
- **Mean (Average)**: Sum of all data points divided by the number of data points.
- **Standard Deviation**: Measure of the amount of variation or dispersion of a set of values.
- **Two-Standard-Deviation Rule**:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1507ef8-c387-4f95-9ab7-d384c0c17d2a%2F0d1e4556-cc17-49f9-8972-b42d1ef33f25%2Fbklmhw_processed.png&w=3840&q=75)
Transcribed Image Text:### Case Study: Determining Reasonable Compensation for Repetitive Stress Injuries
A woman sued a computer keyboard manufacturer, alleging that her repetitive stress injuries were caused by the keyboard. Initially, she was awarded about $3.5 million for pain and suffering. However, the court decided that this award was excessive and sought to establish a reasonable compensation by examining a "normative" group of 27 similar cases.
The court defined a reasonable award to be within two standard deviations of the mean of the awards in the 27 cases, which were as follows (in thousands of dollars):
\[35, 63, 72, 113, 137, 142, 148, 151, 238, 290, 340, 410, 600, 750, 750, 754, 1050, 1100, 1135, 1150, 1200, 1200, 1250, 1577, 1700, 1825, 2000\]
From these values, the sums were calculated as:
\[\sum x_i = 20,180\]
\[\sum x_i^2 = 24,658,024\]
#### Problem Statement:
What is the maximum possible amount that could be awarded under the two-standard-deviation rule? Round your answer to the nearest whole number and input your answer in thousands of dollars.
[Calculate Button]
#### Instructions:
1. **Understand the Dataset**: This data represents previous awards in similar cases. The court aims to identify a reasonable compensation by statistical measures.
2. **Calculate Mean and Standard Deviation**:
- **Mean**: Calculate the mean of the given awards.
- **Standard Deviation**: Compute the standard deviation to understand the spread of the data.
3. **Apply the Two-Standard-Deviation Rule**:
- Determine the range of awards that fall within two standard deviations of the mean.
4. **Find the Maximum Award**: Identify the highest award within this range, rounded to the nearest thousand dollars.
This exercise helps in understanding how courts can use statistical methods to determine reasonable compensation amounts in lawsuits involving financial awards.
### Key Concepts:
- **Mean (Average)**: Sum of all data points divided by the number of data points.
- **Standard Deviation**: Measure of the amount of variation or dispersion of a set of values.
- **Two-Standard-Deviation Rule**:
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