The number of medical emergency calls per hour has a Poisson distribution with parameter λ. A record of emergency calls is available for a sufficient amount of time and parameter λ is assumed to be the same throughout the available recording of calls. Numbers of emergency calls at different hours are considered independent.
If λ = 1, what is the probability of more than 20 emergency calls occur in 10 consecutive hours of a single medical response team shift? If average service last 54 minutes, what is the probability that all calls received in 10 consecutive hours can be served?