Telephone calls can be classified as voice (V) if someone is speaking, or data (D) if there is a modem or fax transmission. Based on a lot of observations taken by the telephone company, we have the following probability model: P[V] = 0.8, P[D] = 0.2. Data calls and voice calls occur independently of one another. The random variable Kn is the number of data calls in a collection of n phone calls.
(a) What is E[K100], the expected number of voice calls in a set of 100 calls?
(b) What is σK100, the standard deviation of the number of voice calls in a set of 100 calls?
(c) Use the central limit theorem to estimate P[K100 ≥ 18], the probability of at least 18 voice calls in a set of 100 calls.
(d) Use the central limit theorem to estimate P[16 ≤ K100 ≤ 24], the probability of between 16 and 24 voice calls in a set of 100 calls.