The number of customers arriving at a grocery store is a Poisson random variable with on average 10 customers arriving per hour. Let $X$ be the number of customers arriving from 10 am to 11:30a m. What is the probability that there are more than 10 but less than or equal to 12 customers arriving between 10 am and 11:30 am ($P(10 < X \le 12)$)?
Do I use the Poisson distribution formula using mean=10 or mean=15 because it is for 1.5 hrs?
And then do I just do $P(10 < X \le 12) = P(X=11) + P(X=12)$ where for $P(X=11)$, $\lambda=15$ and $X=11$, and for $P(X=12)$, $\lambda$ is $15$ and $X=12$.
Because so far I am getting 0.1491 but unsure of which mean to use.