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1. Think about the demographics of Fulton County, Georgia and of the jury selected for the trial of James Avery. a. There were 165,814 African-Americans in the Fulton County population of 691,797. What proportion is this? b. The list of 21,624 potential jurors in the county had 1,115 African-Americans. What proportion is this?

1. Think about the demographics of Fulton County, Georgia and of the jury selected for the trial of James Avery. a. There were 165,814 African-Americans in the Fulton County population of 691,797. What proportion is this? b. The list of 21,624 potential jurors in the county had 1,115 African-Americans. What proportion is this?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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**Educational Website Content: Understanding Binomial Distribution and its Application in Jury Selection** --- **4. Binomial Distribution and Normal Approximation** Recall that the binomial distribution with a probability of success \( p \) is nearly normal when the sample size \( n \) is sufficiently large (when \( np \) and \( n(1-p) \) are both at least 10). **a. Calculating \( np \) and \( n(1-p) \)** The jury pool from which the jury was selected had 60 people. Using the Fulton County population statistics and a sample size \( n=60 \), calculate \( np \) and \( n(1-p) \). Is it reasonable to use the normal distribution to approximate the binomial distribution here? **b. Finding \( \mu \) and \( \sigma \)** Find \( \mu \) (mean) and \( \sigma \) (standard deviation) for this normal distribution. **c. Probability Calculation** Find the probability (under this normal distribution) that there are no African-Americans in the 60-person jury pool. --- **5. Jury Pool Selection Analysis** The jury pool of 60 people was selected from the list of 21,624 potential jurors. Can getting no African-Americans in a jury pool selected from these potential jurors reasonably be attributed to chance alone, or should the lawyers look for another explanation? What strategies could you use to support your choice? --- **6. U.S. Supreme Court Case Review** The U.S. Supreme Court overturned Avery’s conviction. Describe the statistical evidence that you think might have been used by Avery’s lawyers. --- **Educational Insights:** This section explores the application of statistical methods in legal contexts, emphasizing how binomial distribution and normal approximation can provide insights into jury selection processes. Key concepts include calculating expected frequencies, understanding population statistics, and applying probability theory in legal cases to ensure fair trial processes.
Transcribed Image Text:**Educational Website Content: Understanding Binomial Distribution and its Application in Jury Selection** --- **4. Binomial Distribution and Normal Approximation** Recall that the binomial distribution with a probability of success \( p \) is nearly normal when the sample size \( n \) is sufficiently large (when \( np \) and \( n(1-p) \) are both at least 10). **a. Calculating \( np \) and \( n(1-p) \)** The jury pool from which the jury was selected had 60 people. Using the Fulton County population statistics and a sample size \( n=60 \), calculate \( np \) and \( n(1-p) \). Is it reasonable to use the normal distribution to approximate the binomial distribution here? **b. Finding \( \mu \) and \( \sigma \)** Find \( \mu \) (mean) and \( \sigma \) (standard deviation) for this normal distribution. **c. Probability Calculation** Find the probability (under this normal distribution) that there are no African-Americans in the 60-person jury pool. --- **5. Jury Pool Selection Analysis** The jury pool of 60 people was selected from the list of 21,624 potential jurors. Can getting no African-Americans in a jury pool selected from these potential jurors reasonably be attributed to chance alone, or should the lawyers look for another explanation? What strategies could you use to support your choice? --- **6. U.S. Supreme Court Case Review** The U.S. Supreme Court overturned Avery’s conviction. Describe the statistical evidence that you think might have been used by Avery’s lawyers. --- **Educational Insights:** This section explores the application of statistical methods in legal contexts, emphasizing how binomial distribution and normal approximation can provide insights into jury selection processes. Key concepts include calculating expected frequencies, understanding population statistics, and applying probability theory in legal cases to ensure fair trial processes.
**Title: Jury Demographics and Legal Fairness: An Analysis** **The Importance of Jury Demographics** The ethnicity, gender, age, and other demographic characteristics of juries have been of great interest in some trials in the United States. When the composition of a jury does not reflect the demographic characteristics of the surrounding community, doubts about the fairness of the jury selection process and legal challenges can arise. **Jury Selection and Randomness** Although juries are not selected solely by chance, comparing the actual jury to the composition of juries that would occur if jurors were selected at random can tell lawyers whether there are grounds to investigate the fairness of the jury selection process. **Case Study: Avery v. Georgia** A historic case concerning jury selection, *Avery v. Georgia*, was brought to the U.S. Supreme Court in 1953. A jury in Fulton County, Georgia had convicted Avery, an African-American, of a serious felony. There were no African-Americans on the jury. At the time, there were 165,814 African-Americans in the Fulton County population of 691,797. The list of 21,624 potential jurors had 1,115 African-Americans. A jury pool of 60 people was selected, supposedly at random, from the list of potential jurors. (However, the names of black and white jurors had been written on different colored slips of paper.) This jury pool, from which the 12 actual jurors were selected, contained no African-Americans. **Sample Size Guideline** *If the size of a random sample is less than 10 percent of the size of the population from which it is taken, then, without much loss of accuracy, you can ignore the fact that the sampling is without replacement when computing a probability.* **Exercise: Analyzing Jury Demographics** 1. **Think about the demographics of Fulton County, Georgia and of the jury selected for the trial of James Avery.** a. There were 165,814 African-Americans in the Fulton County population of 691,797. What proportion is this? b. The list of 21,624 potential jurors in the county had 1,115 African-Americans. What proportion is this? **Analysis** This educational content highlights the significance of reflecting community demographics within juries to safeguard the integrity and fairness of the legal process.
Transcribed Image Text:**Title: Jury Demographics and Legal Fairness: An Analysis** **The Importance of Jury Demographics** The ethnicity, gender, age, and other demographic characteristics of juries have been of great interest in some trials in the United States. When the composition of a jury does not reflect the demographic characteristics of the surrounding community, doubts about the fairness of the jury selection process and legal challenges can arise. **Jury Selection and Randomness** Although juries are not selected solely by chance, comparing the actual jury to the composition of juries that would occur if jurors were selected at random can tell lawyers whether there are grounds to investigate the fairness of the jury selection process. **Case Study: Avery v. Georgia** A historic case concerning jury selection, *Avery v. Georgia*, was brought to the U.S. Supreme Court in 1953. A jury in Fulton County, Georgia had convicted Avery, an African-American, of a serious felony. There were no African-Americans on the jury. At the time, there were 165,814 African-Americans in the Fulton County population of 691,797. The list of 21,624 potential jurors had 1,115 African-Americans. A jury pool of 60 people was selected, supposedly at random, from the list of potential jurors. (However, the names of black and white jurors had been written on different colored slips of paper.) This jury pool, from which the 12 actual jurors were selected, contained no African-Americans. **Sample Size Guideline** *If the size of a random sample is less than 10 percent of the size of the population from which it is taken, then, without much loss of accuracy, you can ignore the fact that the sampling is without replacement when computing a probability.* **Exercise: Analyzing Jury Demographics** 1. **Think about the demographics of Fulton County, Georgia and of the jury selected for the trial of James Avery.** a. There were 165,814 African-Americans in the Fulton County population of 691,797. What proportion is this? b. The list of 21,624 potential jurors in the county had 1,115 African-Americans. What proportion is this? **Analysis** This educational content highlights the significance of reflecting community demographics within juries to safeguard the integrity and fairness of the legal process.
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