Question

Phone calls can be classified as voice (V) if someone is speaking, or data (D) if there is a modem or fax transmission. Based on many observations made by the telephone company, we have the following probability model: P [V] = 0.8, P [D] = 0.2. Data calls and voice calls are produced independently. The random variable Kn is the number of data calls in a collection of n calls telephone

(a) What is the E [K100], the expected number of voice calls in a set of 100 calls?

(b) What is the 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 16 and 24 voice calls in a set of 100 calls.

Answer 1

In a random sample, Kn is the no of data calls

where d=0 and where d=1 or 0 otherwise

E(D)= 0.2 and Var(D) = 0.2- 0.04 = 0.16

a)

b)

c)

d)