A college has 152 assistant professors, 127 associate professors, and 208 full professors. A journalist with the student newspaper was interested in whether faculty members were actually in their offices during posted office hours. The student journalist decided to investigate samples of 40 assistant professors, 40 associate professors, and 50 full professors. Student volunteers were sent to knock on the doors of these sample members during their posted office hours. It was found that 31 of the assistant professors, 29 of the associate professors, and 34 of the full professors were actually in their offices at these times.
a. Using an unbiased estimation procedure, find a point estimate of the proportion of all faculty members who are in their offices during posted office hours.
b. Find 90% and 95% confidence intervals for the proportion of all faculty members who are in their offices during posted office hours.