A college admissions Office was looking through records of students from the past 5 years and found that out-of-state students had more volunteer hours then in-state students. The distributions of both groups were roughly normal Where the hours for in-state students were distributed with a mean of 85 hours and a standard deviation of 15 hours while they're out-of-state students had a mean of 130 hours and a standard deviation of 30 hours. 70% of students who attend this college are in-state students
a. For a randomly selected in-state student, what is the probability that they have more than 100 volunteer hours?
b. For a randomly selected student from the college, what is the probability that they have more than 100 volunteer hours?
c. Given that a student has more than 100 volunteer hours, what is the probability that the student is out-of-state?