Problem 8 (30 points) According to the Current Population Survey (Internet Release date: September 2004), 42% of females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home). Suppose a survey is administered today to 425 randomly selected females between the age of 18 and 24 years and 204 respond that they live at home. 1. Does this define a binomial distribution? Justify your answer 2. If so, can you use the normal approximation to binomial distribution? Justify your answer and state what the mean and standard deviation of the normal approximation are. 3. Using the binomial probability distribution, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42%? 4. Using the normal approximation to binomial, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42% ?

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Problem 8 (30 points)
According to the Current Population Survey (Internet Release date: September 2004), 42% of
females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college
students living in a dorm are counted as living at home). Suppose a survey is administered
today to 425 randomly selected females between the age of 18 and 24 years and 204 respond
that they live at home.
1. Does this define a binomial distribution? Justify your answer
2. If so, can you use the normal approximation to binomial distribution? Justify your answer
and state what the mean and standard deviation of the normal approximation are.
3. Using the binomial probability distribution, what is the probability that at least 204 of the
respondents living at home under the assumption that the true percentage is 42%?
4. Using the normal approximation to binomial, what is the probability that at least 204 of the
respondents living at home under the assumption that the true percentage is 42% ?
Transcribed Image Text:Problem 8 (30 points) According to the Current Population Survey (Internet Release date: September 2004), 42% of females between the ages of 18 and 24 years lived at home in 2003. (Unmarried college students living in a dorm are counted as living at home). Suppose a survey is administered today to 425 randomly selected females between the age of 18 and 24 years and 204 respond that they live at home. 1. Does this define a binomial distribution? Justify your answer 2. If so, can you use the normal approximation to binomial distribution? Justify your answer and state what the mean and standard deviation of the normal approximation are. 3. Using the binomial probability distribution, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42%? 4. Using the normal approximation to binomial, what is the probability that at least 204 of the respondents living at home under the assumption that the true percentage is 42% ?
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