Question6. The duration of a telephone call (in seconds) has a uniform distribution over the interval $[0,200]$. With probability $1 / 20$, the telephone call is a roaming connection and a proportional charge of 2 cents per second is added; in other cases the telephone cost is included in a monthly standing charge of $\$ 50$. There were 120 independent connections in May. a) Calculate the expected value of the invoice for May. b) Using the Poisson theorem, approximate the probability that at least three calls resulting in extra charges of at least $\$ 1$ each were made.