Suppose I am employed at a college in which 62% of the student population is female. I am currently teaching statistics to 135 students this semester. I would like to select 50 students randomly from this group to participate in one of my research projects.

a. What is the probability that 30 or more students in my sample will be female?

b. What is the probability that 27 or more students in my sample will be female?

c. What is the probability that between 28 and 36 of the students in my sample will be female?

d. Which of the four probability sampling procedures would be most appropriate if gender was an important factor in the research?