Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) Is it likely that the total service time will exceed $2.5$ hours?
Let $S$ be the total service time $= 10Y$. What I have: $$E(S) = 10E(Y) = 70$$ $$V(S) = 100V(Y) = 700$$ $$P(S>150) = P(Y>15) = 1-P(Y\le 15) = 1-.998 = .002$$ So the event is very unlikely to occur.
Is my answer right?