question archive Suppose that 75% of adult Americans agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited
Suppose that 75% of adult Americans agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited
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Suppose that 75% of adult Americans agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited.We will take a random sample of 50 American adults and ask them if they agree with the statement. Then the sampling distribution of the sample proportion of people who answer yes to the question is:
Group of answer choices
neither Normal, not Binomial.
Binomial, with n=50 and p=0.75.
approximately Normal, with mean 0.75 and standard error 0.0612.
approximately Normal, with unknown mean and standard deviation.
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approximately Normal, with mean 0.75 and standard error 0.0612
Step-by-step explanation
The central limit theorem states that even if a population distribution is not normal, its sampling distribution of the sample proportion p^? will be approximately normal for large sample sizes (n > 30).
If so, then
μp^??=p
σp^??=np(1−p)??
We took a random sample of n = 50 American adults and since this is greater than 30, we can apply the Central Limit Theorem. We have the population proportion of p=0.75. Thus, the sampling distribution of the sample proportion of people is approximately normal with
μp^??=p=0.75
σp^??=np(1−p)??=50(0.75)(1−0.75)??=0.06123724357
