**Option 2: Probabilities of Graduation and Publication**

**Instructions**

In the following study, three different universities have been tracking a select group of professors over the course of their employment at that university to determine the number of students who are in a particular professor’s classes, how many of those students have graduated, and if any of them have had their work published. In the attached Excel file, __Probabilities__, are the totals for each of the professors at the three different universities that participated in the study.

The purpose of this study is to find the probabilities of graduation and publication for the students in the different professors’ courses. While a causal relationship may not be found between a professor and student graduation or publication, we need to rank the professors based on the different probabilities found with the data sets as described below.

Prepare a report (see below) with your ranking of the professors based on the probabilities and conditional probabilities as well as the analysis of each university. Include the following seven (7) items in table format which is provided in the __Probabilities__ file to support your ranking.

Note: Be sure to use five (5) decimal places for your probabilities in the table, as some of them will be quite small. Do not convert to percentages as we are interested in probabilities only here.

- The overall probability of students graduating at each of the three universities.
- The overall probability of students having a publication at each of the three universities.
- The overall probability of students having a publication, given that they graduated at each of the three universities.
- The probability of a student graduating for each professor.
- The probability of a student having a publication for each professor.
- The probability of a student having a publication given that they graduated for each professor.
- Rank the professors within each university for each of the probabilities in 4–6. Then find the sum of the ranks and determine an overall ranking for each professor.

**Paper Requirements** Items that should be included, but are not limited Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.

Note: You *must* submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.

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