Suppose it is known that 20% of students at a certain college participate in a textbook recycling program each semester.

a. If a random sample of 50 students is selected, do we expect that exactly 20% of the sample participates in the textbook recycling program? Why or why not?

b. Suppose we take a sample of 500 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 20%: the proportion from a sample size of 50 or the proportion from a sample size of 500? Explain your reasoning.