The Journal of American College Health found that 56.4% of college students who lived in coed dormitories consumed alcohol weekly (compared with 26.5% who lived in single sex dormitories). A random sample of 160 students who live in coed dormitories was selected.

a. What is the probability that more than 50% of the students in the sample consume alcohol weekly?

b. What is the probability that less than 65% of the students in the sample consume alcohol weekly?

c. What impact would changing the sample size to 100 students have on the results in part a?

d. Identify the symmetrical interval that includes 95% of the sample proportions with a sample size of 160 if the true population proportion of students in coed dormitories who consume alcohol weekly is 56.4%.