Question

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:
a approximately Normal, with unknown mean and standard deviation.
b neither Normal, not Binomial.
c Binomial, with n=50 and p=0.75.
d approximately Normal, with mean 0.75 and standard error 0.0612.

Answer 1

With random sample of 50 and probability of adult American agrees is 75%, then the sampling distribution of the sample proportion is the Binomial distribution, with n=50 and p=0.75

We use Binomial distribution when the number of observation is fixed, each observation is fixed and each observation represents an outcome of "success" and "failure". In above case, the number of observation is 50 and the outcome of success is 0.75