Critical Thinking: Jackson County Judges (95 points)
Jackson County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, and of those appealed, some of the cases are reversed. Jackie Chan of The Star Tribune conducted a study of cases handled by Jackson County judges over a three-year period. In the attached Excel file Judges are the results for the 182,908 cases handled (disposed) by 40 judges in Common Pleas Court, Domestic Relations Court and Municipal Court.
The purpose of the newspaper's study was to evaluate the performance of the judges. The newspaper wanted to know which judges were doing a good job and which ones were making too many mistakes. You are to assist in the data analysis by using your knowledge of probability and conditional probability to help with the ranking of the judges as well as each court.
Prepare a report (see below) with your ranking of the judges based on the probabilities and conditional probabilities as well as the analysis of each court. Include the following seven (7) items in table format to support your ranking. Be sure to use five (5) decimal places for your probabilities in the table as some of them will be quite small.
1. The probability of cases being appealed in each of the three different courts.
2. The probability of cases being reversed in each of the three different courts.
3. The probability of cases being reversed given an appeal in each of the three different courts.
4. The probability of a case being appealed for each judge.
5. The probability of a case being reversed for each judge.
6. The probability of reversal given an appeal for each judge.
7. Rank the judges within each court for each of the probabilities in 4 - 6. Then find the sum of the ranks and get an overall ranking for each judge.
Be sure that your report contains the following:
· A title page
· An introduction
· A body of the paper that answers the questions posed in the problem and calculations and graphs associated with this problem.
· A conclusion paragraph that addresses your findings and what you have determined from the data and your analysis.
Be sure to submit your Excel file as well.