More than 40 help-desk calls in ten minutes

Calls reach a help desk as a Poisson process averaging $270$ per hour. What is the probability that strictly more than $40$ calls arrive during the coming $10$ minutes? Give three decimal places.

$0.744$. Ten minutes is one sixth of an hour, so the count is Poisson with mean $45$. The chance of $40$ or fewer arrivals is about $0.256$, so the complement, strictly more than $40$, is about $0.744$.