A telephone poll of 1000 adult Americans was reported in a magazine, One of the questions asked was "What is the main problem facing the country?" Suppose 30%s answered "crime". We are interested in the population proportion of adult Americans who feel that crime is the main problem, NOTE: If you are using a Student's I-distribution, you may assume that the underlying population is normally distributed In general, you must first prove that aspumption, though) Define the Random Variables X and P, in words. ( I'm the number of adult Americans who feel that crime is the main problem, and P" is the proportion of adult Americans who feel that crime is the main problem. O *'B the number of people who think there are problems facing the country, and A" is the proportion of people who think there are problems facing the country I'm the number of adults that read the magazine, and A is the proportion of adults who read the magazine. (1 *'is the proportion of adult Americans who feel that crime is the main problem, and P is the number of adult Americans who feel that crime is the main problem Fan ibj which distribution should you use for this problem? (Round your answers to these decimal places) Explain your choice. O The Student's /-distribution should be used because we do not know the standard deviation. ( The binomial distribution should be used because the two outcomes are "crime is the main problem and "crime is not the main problem" ( The standard normal datribution should be used because we are interested in proportions and the simple tie is large. The standard normal diantribution should be used because spy 2 10. Pam Ing Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem. In State the confidence interval. (Round your answers to four decimal places.) In Sketch the graph C.L. = P' Fill Calculate the error bound. [Round your answer to four decimal places.)