The University of Jordan, the Middle East, is counting the mean research papers published per year by its faculty members—professors, senior lecturers, and lecturers. The university has 55 professors, 250 senior lecturers, and 845 lecturers. Random samples of 20 professors, 80 senior lecturers, and 150 lecturers were selected. The sample means of published research papers were 110 professors, 95 senior lecturers, and 100 lecturers. The sample standard deviations were 1.05, 2.52, and 1.58, respectively.

a. Using an unbiased estimation procedure, find the mean number of research paper published by the university per year.

b. Find a 90% confidence interval for the mean research papers published per year by the university.