American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 50.0% 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-1. What is the random variable? The random variable is the count of the households that have a landline. a-2. How is the random variable distributed? The random variable follows a probability distribution. b. What is the probability that none of the households in the sampled group have landline phone service? Note: Round your answer to 4 decimal places. Probability c. What is the probability that exactly five of the households in the sampled group have a landline phone service? Note: Round your answer to 4 decimal places. Probability d. Given the probability distribution, what is the mean number of households with landline service? Note: Round your answer to 3 decimal places. Mean e. What is the variance of the probability distribution of the number of households with landline service? Note: Round your answer to 3 decimal places. Variance
American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 50.0% 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-1. What is the random variable? The random variable is the count of the households that have a landline. a-2. How is the random variable distributed? The random variable follows a probability distribution. b. What is the probability that none of the households in the sampled group have landline phone service? Note: Round your answer to 4 decimal places. Probability c. What is the probability that exactly five of the households in the sampled group have a landline phone service? Note: Round your answer to 4 decimal places. Probability d. Given the probability distribution, what is the mean number of households with landline service? Note: Round your answer to 3 decimal places. Mean e. What is the variance of the probability distribution of the number of households with landline service? Note: Round your answer to 3 decimal places. Variance
Chapter9: Sequences, Probability And Counting Theory
Section9.7: Probability
Problem 4SE: What is the difference between events and outcomes? Give an example of both using the sample space...
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Transcribed Image Text:American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 50.0% 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-1. What is the random variable?
The random variable is the count of the
households that have a landline.
a-2. How is the random variable distributed?
The random variable follows a
probability distribution.
b. What is the probability that none of the households in the sampled group have landline phone service?
Note: Round your answer to 4 decimal places.
Probability
c. What is the probability that exactly five of the households in the sampled group have a landline phone service?
Note: Round your answer to 4 decimal places.
Probability
d. Given the probability distribution, what is the mean number of households with landline service?
Note: Round your answer to 3 decimal places.
Mean
e. What is the variance of the probability distribution of the number of households with landline service?
Note: Round your answer to 3 decimal places.
Variance
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Step 1: Determine the given variables.
VIEWStep 2: Determine the random variable and it's distribution.
VIEWStep 3: Find the probability that none of the household have landline phone service.
VIEWStep 4: Find the probability that exactly 5 households have a landline phone service.
VIEWStep 5: Find the mean no. of households with landline service.
VIEWStep 6: Find the variance of the probability distribution.
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