8.80 Changing majors during college. In a random sample of 975 students from a large public university, it was found that 463 of the students changed majors during their college years.

1. (a) Give a 95% confidence interval for the proportion of students at this university who change majors.

2. (b) Express your results from part (a) in terms of the percent of students who change majors.

3. (c) University officials concerned with counseling students are interested in the number of students who change majors rather than the proportion. The university has 37,500 undergraduate students. Convert the confidence interval you found in part (a) to a confidence interval for the number of students who change majors during their college years.