An IAB study on the state of original digital video showed that original digital video is becoming increasingly popular. Original digital video is defined as professionally produced video intended only for ad-supported online distribution and viewing. According to IAB data, 30% of American adults 18 or older watch original digital videos each month. (Data extracted from IAB Original Digital Video Consumer Study: April 2015, bit.ly/1MtVhwL.)

a. Suppose that you take a sample of 100 U.S. adults. If the population proportion of U.S. adults who watch original digital videos is 0.30, what is the probability that fewer than 25% in your sample will watch original digital videos?

b. Suppose that you take a sample of 500 U.S. adults. If the population proportion of U.S. adults who watch original digital videos is 0.30, what is the probability that fewer than 25% in your sample will watch original digital videos?

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).