Calculating the probability using Poisson Distribution > During working hours, an office switchboard receives telephone calls at random and at an average of 3 calls per minute. > > a) What is the expected number of calls received during a five minute period? Ans: Let X = number of calls per minute therefore $\Bbb E[X] = 3$. During a five minute period, $5\,\Bbb E[X] = 15$ expected calls. > b) What is the probability that exactly the expected no. from (a) are received in a five minute period? Ans: Let $Y$ = number of calls during a five minute period therefore from the previous question, $\Bbb E[Y] = 15$. So, $\Bbb P(Y = 15) = 15^{15}\,\mathsf e^{-15} / 15!$ Are the answers right? Thanks!

Yes, that is correct. There is not much more to say.