"Do you believe your children will have a higher standard of living than you have?" This question was asked of a national sample of American adults with children in a Time/CNN poll (lan. 29, 1996). Sixty-three percent answered in the affirmative, with a margin of error of plus or minus 3%. Assume that the true percentage of all American adults who believe their children will have a higher standard of living is 50. Let X represent the number in a random sample of fifteen American adults who believe their children will have a higher standard of living. a. What are the expected value and standard deviation of X? Show your work. (4 points) b. Find the probability that ten American adults believe their children will have a higher standard of living. Show your work. (4 points) c. Suppose fifty American adults are selected at random. Also suppose now that the true percentage of all American adults who believe their children will have a higher standard of living is .03. Let X represent the number in a random sample of fifty American adults who believe their children will have a higher standard of living. (i) What is the expected value and standard deviation of X? Show your work. (3 points) (iii) Use the appropriate approximation to find the probability that more than five believe their children will have a higher standard of living? Show your work. (4 points)