SOLUTION: 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 de
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Question 1202772: 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.
a. What is the probability that exactly five of the households in the sampled group have a landline phone service?
b. Given the probability distribution, what is the mean number of households with landline service?
c. What is the variance of the probability distribution of the number of households with landline service? Answer by ikleyn(52810) (Show Source):
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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.
(a) What is the probability that exactly five of the households in the sampled group
have a landline phone service?
(b) Given the probability distribution, what is the mean number of households with landline service?
(c) What is the variance of the probability distribution of the number of households with landline service?
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It is a standard binomial distribution probability problem.
The number of trials n= 8. The probability of success at each individual trial is p= 0.53.
(a) P = = = 0.2431 (rounded). ANSWER
(b) the mean number of households with landline service is
np = in this problem = 0.53*8 = 4.24 (exact value). ANSWER
(c) the variance of the probability distribution of the number of households with landline service is
n*p*(1-p) = in this problem = 8*0.53*(1-0.53) = 1.9928 (exact value). ANSWER
Solved.
The relevant formulas you can find in any standard textbook on the subject.
