Professors have hundreds of students in their classes each year. Some professors teach only upper-division courses to students who are in their major course of study. Of this group of students, some will graduate and some will be published.

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.

1. The overall probability of students graduating at each of the three universities.
2. The overall probability of students having a publication at each of the three universities.
3. The overall probability of students having a publication, given that they graduated at each of the three universities.
4. The probability of a student graduating for each professor.
5. The probability of a student having a publication for each professor.
6. The probability of a student having a publication given that they graduated for each professor.
7. 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.

Be sure to critically analyze the above calculations in your body paragraphs, explaining how you found each type of probability and then the results you obtained. Be sure to also explain your criteria for ranking in steps 4–7, and defend why you chose that ranking method—as your way might not be the typical method.