In a math class, the professor shows a list of grades without names to summarize class performance on the quiz. The grades are: 55, 30, 96, 57, 50, 40, 40, 23, 59, 30, 95, 80, 65, 41, 34, 20, 49, 39, 43, 95, 4, 38, 45, 45, 34, 90. a) Alice wants to learn her grade before the professor announces grades with names and she believes that she did better than 72% of the class. If her claim is true, what is the minimum grade she should expect? b) The professor gave Alice a clue by saying that she had scored around 70 points. Find the percentile rank using the method covered in class AND the direct definition of the percentile. (Note: You have to provide 2 different solution approaches, not one.)