The article “Fewer Americans Are Reading, But Don’t Blame the Millennials” (Los Angeles Times, October 9, 2016) indicates that 80% of millennials (those age 18 to 29) have read a book in the last year. Suppose that this is the actual percentage for the population of all millennials. Consider a sample proportion p̂ that is based on a random sample of 225 millennials.

a. If p = 0.80, what are the mean and standard deviation of the sampling distribution of p̂?

b. If p = 0.70, what are the mean and standard deviation of the sampling distribution of p̂?

c. Is the sampling distribution of p approximately normal in both cases (p = 0.80 and p = 0.70)?