The problem is as follows:
The daily concentration of a certain pollutant in a stream has an exponential distribution with a daily mean of 2 mg/l. Suppose that the problem of pollution will occur if the concentration of the pollutant exceeds 6 mg/l.
a) What is the probability of pollution resulting from this pollutant in a single day?
b) What is the return period (in days) associated with this concentration level of 6 mg/l?
c) What is the probability that this pollutant problem will occur at most once in the next 3 days?
For part a I used Poisson Distribution.
For part b I should get an answer of 20 days but I can't find how.
For part c I should get an answer of 0.993 but I don't get the same answer. I used Bimomial with the probability I found on part a and with n=3.
I think there is something wrong with the question. I think they meant at least 6 and not exceeds 6. The answers do not match. I am really confused..
Thank you in advance.