# Probability of observing a certain amount of arrivals in an interval

I'm told the mean rate of arrivals in a facility is 10 per minute.

I'm asked to find the probability that more than 2 arrivals occur within 10 seconds.

I know that $$P(>2$$ arrivals$$) = 1-P(<=2$$ arrivals$$)$$ but since the interval is 10 seconds and not 60 I'm a bit confused.

If they asked what the probability of more than 2 arrivals in 60 seconds was I could just use the Poisson table.

In order to answer this question do I just convert my mean rate? So instead of 10 per minute it could be $$10/6$$ arrivals per 10 seconds and then use the poisson table?

I'm just a bit confused on what to do when the mean rate is given as 'per minute' and the question is only looking at a 10 second interval.

I hope I've explained it well enough, any help would be appreciated.

• As you say, a rate of $10$ per minute is a rate of $10/6$ arrivals per $10$ seconds. You seem to be assuming a Poisson process Jun 10, 2021 at 17:29
• Ok, so I can use a mean rate of 10/6 and then just use the poisson table? Jun 11, 2021 at 12:08