I have the following problem:
A mail server, sends emails with rate $7.5/\text{hour}$.
What is the probability that it will send exactly $5$ emails in one hour?
To solve it, I did the following using a Poisson distribution:
$\frac{7.5^5 e^{-7.5}}{5!}$
or with sage math:
def dpoi(x): return (7.5^x * (e^-7.5)) / factorial(x) dpoi(5) 0.109374594682555$$
is that right?