Question

American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 53.0% of American households still have landline phone service. We decide to randomly call eight households and ask if the home has a landline phone.

Required:
a. What is the random variable?
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?

Answer 1

Solution :

a). According to the reports, 53.0% of the American households still have a landline phone service. Out of which 8 households are randomly called.

Here, the landline phone service is p = 53.0%

                                                           n = 8

Therefore, q = 1 - p

                     = 1 - 0.53

                     = 0.47

here we use the binomial distance because the probability of having the landline phone service is constant and the number of the trial are finite.

b). Let x be the number of household in the sample group having landline phone service.

  Probability that none of the household in the sample group have a landline service is

= P( x = 0)

$=^8C_0 (0.53)^0(0.47)^8$

= 0.002 (using the binomial calculation )

c). Probability that exactly 5 of the household in the sample have a landline service is given by :

 P(x = 5)

$=^8C_5 (0.53)^5(0.47)^3$

= 0.24