I'm not certain how to answer these.
It says that the number of events in $t$ units of time has Poisson Distribution with parameter $\lambda$.
The waiting time between two events has exponential distribution with scale (time per event) $\beta$ = 1$/$ $\alpha$.
Waiting time for $kth$ event has Gamma Distribution with shape $k$ and scale $\beta$.
The actual question: On average 3.64 people arrive per minute according to the Poisson Process.
A) Probability that the first person to arrive takes more than 10 seconds. I wrote 1-ppois(10,3.5) = .0014, but that's obviously wrong.
B) Probability that more than 6 people arrive in a minute. I wrote 1-ppois(6,3.5) = .0766.
C) Consider the distribution of the time at which the 12th person arrives. Find the .95 quantile. I'm not certain if I'm supposed to use the normal Poisson Distribution or the Gamma Distribution.
D) The probability that the 12th person has not arrived after 5 minutes. I'm not really sure what to do here.
Too much information in the problem. I don't know what's relevant. Thank you for any help.