The time it takes a student to walk from the dorm to the chemistry lab follows roughly a Normal distribution with a mean of 20 minutes and a standard deviation of 3 minutes. Suppose you are waiting for your friend at the chemistry lab. She is walking from the dorm to the lab. Fifteen minutes have already passed since the time she left the dorm. What is the probability she will arrive at the chemistry lab in the next 10 minutes (for a total walking time of less than 25 minutes) a. What proportion of students is faster than 15 minutes when walking from the dorm to the chemistry lab?
b. How long does it take the slowest 10% of the students to walk from the dorms to the chemistry lab?