Desertland Hospital in Arizona keep records of its emergency room traffic. Those records indicate that, beginning at 6:00 PM on any given day, the average time until a patient arrives is 10.2 minutes. Each patient arrival is independent.

a. On a particular day, what is the probability the first patient arrives before 6:15 PM? What distribution and parameter(s) are you using?

b. What is the probability that first patient arrives after 6:08 PM?

c. What is the probability that the first patient arrives between 6:15 PM and 6:30 PM?

d. Given a patient arrives after 6:10 PM, what is the probability the first patient arrives before 6:21 PM? Find the median time to the first arrival. What time is that on the clock?