Internet packets can be classified as video (V) or as generic data (D). Based on a lot of observations taken by the Internet service provider, we have the following probability model: P[V] = 0.8, P[D] = 0.2. Data packets and video packets occur independently of one another. The random variable Kn is the number of video packets in a collection of n packets.
(a) What is E[K48], the expected number of video packets in a set of 48 packets?
(b) What is σK48, the standard deviation of the number of video packets in a set of 48 packets?
(c) Use the central limit theorem to estimate P[30 ≤ K48 ≤ 42], the probability of between 30 and 42 voice calls in a set of 48 calls.
(d) Use the De Moivre-Laplace formula to estimate P[30 ≤ K48 ≤ 42].