Suppose that a compagnie has in average $48$ calls each hours. How many calls the compagnie has in average in $24$ hours.
Attempts
Let $X_n$ the numbers of call during time $n$ and $n+1$ for $n\in \{0,...,23\}$. Each $X_n$ are independent, and thus, the average of the numbers of call in $24$ hours is $24\mathbb E[X_1]$.
In the solution of my exercise, they say that $X_n$ follows a Poisson distribution with parameter $48$, and thus the number of calls in $24$ hours is in means $1152$. But I don't understand why $X_n$ follow a Poisson distribution with parameters $48$. My teacher assistant said that the numbers of call in one hours is a rare event, but I'm not sos satisfied but it in the sense that $48$ calls in $1$ hours, is not so rare...