According to the High School Athletics Participation Survey, approximately 55% of students enrolled in high schools participate in athletic programs. You are performing a study of high school students and would like at least 11 students in the study to be participating in athletics.
(a) How many high school students do you expect to have to randomly select?
(b) How many high school students do you have to select to have a 99% probability that the sample contains at least 12 who participate in athletics?