1. Let's say that a student's arrival time for a statistics class is uniformly distributed where the instructor can show up at any time between 15 minutes early and 5 minutes late. a. Draw a probability density function for the above problem (pdf). b. What is the probability the student will show up between 5 minutes early and on time inclusive? c. What is the probability the student will show up between 5 minutes early and on time not inclusive? d. What is the probability that the student shows up exactly 1 minute early to class? e. What arrival time corresponds to the first quartile? f. What arrival time corresponds to the fifteen percentile? (The number representing the earliest 15 percent)