A student is planning to take the scholastic aptitude test (SAT) exam to gain admission to a top college. She hopes to keep taking the exam until she gets a score of at least 1350 and then she will stop. Her score in any of the exams is uniformly distributed between 1100 and 1500, and her score in one exam is independent of her score in any other exam.
a. What is the probability that she reaches her goal of scoring at least 1350 points in any exam?
b. What is the PMF of the number of times she will take the exam before reaching her goal?
c. What is the expected number of times she will take the exam?