According to a recent Pew Internet & American Life Project Survey (October 2010), 67% of adults who use the Internet have paid to download music. In a random sample of n = 1,000 adults who use the Internet, let p represent the proportion who have paid to download music.
a. Find the mean of the sampling distribution of p̂.
b. Find the standard deviation of the sampling distribution of p̂.
c. What does the Central Limit Theorem say about the shape of the sampling distribution of p̂?
d. Compute the probability that p̂ is less than .75.
e. Compute the probability that p̂ is greater than .50.