Have this question in math statistics Normal Distribution.
In a certain cellular phone system new calls arrives with exponential distributed interarrivaltimes with expectation value $$\mu =\frac{1}{\lambda }=3minutes.$$ The interarrivaltime is the time between two incoming calls.
How do I find the number of incoming calls during one hour?
Perhaps i misunderstand the question but:
The Poisson distribution expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event and is defined as
$\pi(x=k)=\frac{\lambda^ke^{-\lambda}}{k!}$
so your interval time is $\lambda=60/3 = 20$.
The mean of the Poisson is given by $\lambda$ so that is the expected value.
But using the Poisson distribution allows you to answer more interesting questions than just he expected value such as, what is the probability of observing 15 calls in an hour
which is
$\pi(x=15)=\frac{20^{15}e^{-20}}{15!}\approx0.05$ or 5%