A call centre gets an average of 5 calls per minute. Assuming the number of calls received can be modelled by a poisson process, find probability that call centre will receive
i) more than two calls in one minute
ii) will receive 20 calls in 5 minutes
Attempt
i) Using, $\frac{e^{-\lambda}\lambda^{k}}{k!}$, where $\lambda$ is the mean. The probability of less than or equal to two calls in one minute $P(\le 2)$ = P(0) +P(1) +P(2) = $\frac{e^{-5}5^{0}}{0!} $ + $\frac{e^{-5}5^{1}}{1!} $ + $\frac{e^{-5}5^{2}}{2!} $. Therefore the probability of more than two calls = $1 - P(\le 2)$ ? I am not sure if this is correct?
ii) In this case, $\lambda = 5\times5 = 25$. So $P(k = 20) = \frac{e^{-25}25^{20}}{20!}$. Is this the right approach?