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. 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 using 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 retain and report five (5) decimal places for each of your probabilities. Do not convert your computed probabilities to percentages, as we are only interested in probabilities 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 that you obtained. Be sure to also explain your criteria for ranking in steps 4-7, being sure to defend why you chose that particular ranking method, as your way might not be the typical method. Requirements: · Your paper should be 2-3 pages in length (not counting the title page and references page) and cite and integrate at least one credible outside source. · Include a title page, introduction, body, conclusion, and a reference page. o The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic. o The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment. o The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. · Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables or graphs.)MTHCT3

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