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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.

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  • $\begingroup$ 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 $\endgroup$
    – Henry
    Jun 10, 2021 at 17:29
  • $\begingroup$ Ok, so I can use a mean rate of 10/6 and then just use the poisson table? $\endgroup$
    – Charlie P
    Jun 11, 2021 at 12:08

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