Question. 1 pl n a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5. An analysis (a) Explain why a large sample size is necessary to construct a confidence interval for the mean age that people would like to live. (b) Construct and interpret a 95% confidence interval for the mean. (c) How many adult Americans would need to be surveyed to estimate the mean age that people would like to live to within 2 years with 95% confidence? (a) Choose the correct answer below. A. According to the Bayes' Theorem, the sampling distribution of x is approximately binomial when the sample size is large. O B. According to the Central Limit Theorem, the sampling distribution of x is approximately normal when the sample size is large. O C. According to the Law of Averages, the sampling distribution of x is approximately binomial when the sample size is large. O D. According to the Law of Large Numbers, the sampling distribution of x is approximately normal when the sample size is large. (b) the would like to live is between and years. (Type integers or decimals rounded to two decimal places as needed. Use ascending order.) (c) A sample size of n = is required to estimate the mean age that adult Americans would like to live within 2 years with 95% confidence. (Round up to the nearest whole number.)