A telephone poll of 1,000 adult Americans was reported in an issue of Time Magazine. One ofthe questions asked was “What is the main problem facing the country?” Twenty percentanswered “crime.” We are interested in the population proportion of adult Americans who feelthat crime is the main problem.a. Define the random variablesXandPin words.b. Which distribution should you use for this problem? Explain your choice.c. Construct a 95% confidence interval for the population proportion of adult Americans whofeel that crime is the main problem.i. State the confidence interval.ii. Sketch the graph.iii. Calculate the error bound.d. Suppose we want to lower the sampling error. What is one way to accomplish that?e. The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ± 3%. Inone to three complete sentences, explain what the ± 3% represents.