A survey of adults in a certain country found that 77% believed that protecting the rights of those with unpopular views is a very important component of a strong democracy. Assume the sample size was 1200. Complete parts (a) through (f) below. a. How many people in the sample felt this way? The number of people in the sample that felt protecting the rights of those with unpopular views is a very important component of a strong democracy is. (Round to the nearest integer as needed.) b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions are met. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to the nearest integer as needed.) A. Yes, the sample size is large enough, since the expected number of successes is and the expected number of failures is , both of which are greater than or equal to 10. O B. No, the sample size is not large enough, since the estimated standard error is , which is less than 10. C. Yes, the sample size is large enough, since the estimated standard error is , which is greater than or equal to 10. D. No, the sample size is not large enough, since the expected number of successes is |and the expected number of failures is , at least one of which is less than 10. c. Find a 95% confidence interval for the proportion of adults in the country who believe that protecting the rights of those with unpopular views is a very important component of a strong democracy. The 95% confidence interval is (). (Round to three decimal places as needed.) d. Find the width of the 95% confidence interval. The width of the 95% confidence interval is (Round to three decimal places as needed.) e. Now assume the sample size was 4800 and the percentage was still 77%. Find a 95% confidence interval and report the width of the interval. The 95% confidence interval is (). (Round to three decimal places as needed.) What is the width of the interval? The width of the 95% confidence interval is (Round to three decimal places as needed.) f. What happened to the width of the confidence interval when the sample size was increased? Did it increase or decrease? When the sample size is increased the width of the interval increased. decreased. remains the same