American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 49.2% of American households still have landline phone service. We decide to randomly call eight households and ask if the home has a landline phone.

a. What is the random variable? How is the random variable distributed? Why?

b. What is the probability that none of the households in the sampled group have landline phone service?

c. What is the probability that exactly five of the households in the sampled group have a landline phone service?

d. Given the probability distribution, what is the mean number of households with landline service?

e. What is the variance of the probability distribution of the number of households with landline service?