Problem 2 [24 points]: Consider a new proposed antibiotic is taken by 16 patients, and their serum-creatinine level are measured 24 hours after. Assume that the serum-creatinine level is normally distributed, and the sample mean of serum-creatinine level was 1.50 mgde and sample variance of serum-creatinine level was 0.0184. Surgmse that the standard deviation of serum-creatinine level in population is known at 0.28 m dl. (a) [3 points] Construct a 95% Condence Interval for the mean serum-creatinine level .11. lb] [4 points] Instead of using the mm; = 4.96 and znm =1.96 to construct the 95% Confidence Interval for p in part [a], construct another 95% Condence Interval for ,1: based on Zoo; and 2.1.9; lie. 2"" and 97'\" percentile of N {0.1)}. (cl [4 points] Compare part lb} to part (a), what's the difference between these two condence intervals? which condence intervals provide a more accurate estimation? Why? [Why we commonly use Symmetry setting (2\