InstructionsIn 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.

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.

Paper RequirementsItems 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.

University/College Professor/Instructor Number Students Taught Graduated Publications P(Graduated) Rank by P(G) P(Publications) Rank by P(P) P(P|G) Rank by P(P|G) Sum of Ranks Overall RankWWCC J.W. Blake 971 971 466 K.R. Cunningham 1292 1008 433 R.H. Doughty 361 357 154 L.M. Edwards 1072 997 359 W.H. Greiner 1456 1340 389 I.D. Jackson 2352 2352 1058 O.P. Lawson 1911 1701 680 G.F. Nelson 1951 1795 574 A.F. Paul 1608 1254 514 D.K. Raulson 1042 979 264 T.R. South 304 286 129 E.A. Thomas 1119 873 419 C.F. Viney 351 281 135 F.E. Yousef 1123 898 359 Totals EWCC A.D. Blaise 824 766 368 I.A. Frank 1012 860 215 S.D. Gundel 2030 1624 698 P.O. Hogan 2241 1838 515 W.M. Kraft 2133 1642 673 L.I. Luebbers 2253 1983 535 J.H. Nye 190 162 75 J.A. O’Dell 1736 1614 484 R.W. Pauly 2795 2543 839 K.G. Ross 2949 2241 986 D.S. Smith 1918 1918 633 J.P. Trost 715 615 191 M.M. Wall 2859 2830 764 Totals NWCC D.H. Allen 2726 2644 899 T.G. Black 1975 1699 578 M.A. Carter 1098 977 420 M.P. Drake 1468 1321 396 J.K. Elmsworth 1066 810 219 P.T. Grey 1981 1961 922 C.R. Heines 218 172 65 D.R. Jones 1129 1084 358 B.M. Keith 2379 2046 818 G.H. Matheson 2345 1899 874 P.R. Neighbors 1165 967 377 S.T. Orion 2081 1873 693 A.P. Tracey 708 694 250 Totals