The overall probability of students graduating at each of the three universities.
=P (Graduating at WWCC+ graduating at EWCC + graduating at NWCC)
0.86452+ 0.85264 +0.88102 = 2.59818
The overall probability of students having a publication at each of the three universities
=P (publishing at WWCC+ publishing at EWCC + publishing at NWCC)
= 8438/2611 + 5868/18546 + 8014/25777 = 3.85901
The overall probability of students having a publication, given that they graduated at each of the three universities.
=P (student publishing/graduated)
= P (a student having a publication * graduated)/ P (a student graduated from each university)
(0.86452*(8438/2611)/0.86452) + 0.85264*( 5868/18546 )/0.85264) +(0.88102* ( 8014/25777)/0.88102) = 3.85901
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The probability of a student graduating for each professor.
Attached in the excel file
The probability of a student having a publication for each professor
Attached in the excel file
The probability of a student having a publication given that they graduated for each professor.
=P (student publishing/graduated)
= P (a student having a publication * graduated)/ P (a student graduated for each professor)
(12.31036* 4.51436/ 12.31036) + (11.31012* 4.13191/ 11.31012) +( 11.28996*4.06063/1.28996) = 12.70690
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.
Attached in the excel file
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.
Probability is simply chance or likelihood of an event occurring (Sternstein, 2005 ). In order to calculate the probability that an event will happen, you take the total number of successful outcomes divided by the total number of outcomes. Therefore, in calculating the overall probability of students graduating at each of the three universities, the number of successful outcomes is taken for each university and in this case the successful outcome is that of a student graduating then this value is divided by the total number of outcomes which in this case is the total number of students at each university. The addition is finally done to get the overall probabilities of graduating students at the three universities. i.e. the total number of students graduating from WWCC College is 22,660 and the total number of students at the same facility is 26,211 the probability of a student graduating here is therefore 22660/26211 =0.86452. the same is done for all three universities to obtain 0.86452+ 0.85264 +0.88102 = 2.59818.
The same principle is used for the second question to obtain the overall probability of students having a publication at each of the three universities. The number of successful outcomes here is the number of the students who managed to publish and the total number of an outcome being the total number of students at the University. Division is carried out like in the first question then summed for all three universities to obtain the overall probability.
In the third question where one is supposed to calculate the overall probability of students having a publication, given that they graduated at each of the three universities, one has to use the conditional probability formula. A conditional probability is the likelihood of an event occurring given that another has successfully occurred (Moss, & Owen, 1976). Thus, one first obtains the probabilities of a student publishing and graduating then dividing the result by the probability that the student graduated. P (a student having a publication * graduated)/ P (a student graduated from each university). Addition is finally done to get the overall probabilities of students publishing given they had graduated.
To calculate the probability of a student graduating for each professor one divides the number of students who graduated for a particular professor then dividing the result by the total number of students the professor handled and the same is done in calculating the probability of a student having a publication for each professor. For one to calculate the probability of a student having a publication given that they graduated for each professor. The same concept of conditional probability is used (Donnelly, & Abdel-Raouf, 2016) .
In order to rank the professors within each university for each of the probabilities, then one has to find the sum of the ranks within each university. This is achieved by ranking them according to their probabilities in publishing and also probabilities in the number of their students who graduated. These results are then arranged in a descending order starting from the largest to the smallest. The professor who has the largest probability after the sum of ranks has been done, is ranked higher than the rest. This ranking method was chosen because it includes the aggregate score or probabilities of the professors and not just ranking them in terms of one criterion.
References
Donnelly, R., & Abdel-Raouf, F. (2016). Statistics (1st ed.). Indianapolis, Indiana: Alpha, a member of Penguin Random House LLC.
Moss, P., & Owen, P. (1976). Statistics alive (1st ed.). Cambridge, Eng.: Hobsons Press (Cambridge) Ltd. [for] CRAC.
Sternstein, M. (2005). Statistics (1st ed.). Hauppauge, NY: Barron's.
