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 .5, what are the mean value and standard deviation of p^ ? Answer this question for p 5 .6. Doesp^ have approximately a normal distribution in both cases? Explain.

b. Calculate P( p^ $ .6) for both p 5 .5 and p 5 .6.

c. Without doing any calculations, how do you think the probabilities in Part (b) would change if n were 400 rather than 225?