stat problem

Suppose people join a zoom call according to an approximate Poisson process at a mean rate of 12 per hour. Let Z denote the waiting time in minutes until the first person joins the zoom call. Hint: Be careful with the units. 1. How is Z distributed? 2. What is the probability density function of Z? 3. Suppose you are hosting the zoom call. What is the probability that you have to wait less than 2 minutes for the first person to join? 4. Suppose 5 minutes have already passed since you started waiting for the first person to join. What is the probability that the first person will join after 7 minutes since you began waiting? 5. What is the expected amount of time you will wait for the first person to join the call