(Use this problem for questions 36-40.) The Human Resources Department of a large industrial manufacturer is examining the promotion practices in the Engineering Department for engineers who have worked at the company for 10 years. This is the typical point in the company when an engineer is promoted to a "Company Vice President" or given the signal to begin looking for employment elsewhere. There is a suspicion that, among engineers with consistently similar high performance reviews, the ones with the higher educational levels are being promoted more frequently than the ones with lesser educational credentials. A statistician went back through the employment records of the past 5 years and randomly selected 1,000 engineers who had worked at the company for 10 years, who had been consistently rated "high performers," and who were either promoted or not promoted. Among these 1,000 engineers, the statistician found the following information about highest level of educational attainment and rates of promotion: * Among the 550 engineers with a Ph.D. degree, 450 of them were promoted at the 10-year mark, and the others were not and left the company. * Among the 450 engineers with a Bachelor's degree, 100 of them were promoted, and the others were not and left the company. 36. In the space below construct the necessary probability tables to reflect the marginal, joint, and conditional probabilities associated with the sample results. (6 points) Use your table to answer questions 37-40. 37. Given that the engineer holds a Ph.D., what is the probability s/he was promoted? (2 points) 38. Given that the engineer holds a Bachelor's degree, what is the probability s/he was not promoted? (2 points) 39. Given that the engineer was promoted, what is the probability s/he holds a Bachelor's degree? (2 points) 40. Given that the engineer was not promoted, what is the probability s/he holds a Ph. D.? (2 points)