Surveying the Faculty. The faculty of a college consists
of 820 members. A new president has just been appointed.
The president wants to get an idea of what the
faculty considers the most important issues currently facing
the school. She does not have time to interview all the
faculty members and so decides to stratify the faculty by
rank and use stratified random sampling with proportional
allocation to obtain a sample of 40 faculty members. There
are 205 full professors, 328 associate professors, 246 assistant
professors, and 41 instructors.
a. How many faculty members of each rank should be selected
for interviewing?
b. Use Table I in AppendixAto obtain the required sample.
Explain your procedure in detail.

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For the number of professors in each rank I would use a percentage for each rank against the total number of professors.