The article “Thrillers” (Newsweek, April 22, 1985) stated, “Surveys tell us that more than half of America’s college graduates are avid readers of mystery novels.” Let p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion p^ that is based on a random sample of 225 college graduates.
a. If p = .5, what are the mean value and standard deviation of p^? Answer this question for p = .6. Does p^ have approximately a normal distribution in both cases? Explain.
b. Calculate P( p^ ≥ .6) for both p = .5 and p = .6.
c. Without doing any calculations, how do you think the probabilities in Part (b) would change if n were 400 rather than 225?