A survey of 2,250 American adults reported that 59% got news both online and offline in a typical day. (Data extracted from "How Americans Get News in a Typical Day," USA Today, March 10, 2010, p. 1A.)
a. Suppose that you take a sample of 100 American adults. If the population proportion of American adults who get news both online and offline in a typical day is 0.59, what is the probability that fewer than half in your sample will get news both online and offline in a typical day?
b. Suppose that you take a sample of 500 American adults. If the population proportion of American adults who get news both online and offline in a typical day is 0.59, what is the probability that fewer than half in your sample will get news both online and offline in a typical day?
c. Discuss the effect of sample size on the sampling distribution of the proportion in general and the effect on the probabilities in (a) and (b).