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)
= 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)
= 0.24