Question 2 (20 points) Suppose that n = 100 random samples of water from a freshwater lake were taken and the calcium concentration (milligrams per liter) measured. Suppose the measurements follows a normal distribution with a unknown mean a and a known variance of. Suppose the sample mean is 0.655 and / E (-co, 0.82] is a 95% upper confidence bound on the mean calcium concentration. (a) What is the value of the known variance o-? (b) Would a 99% upper confidence bound calculated from the same sample data be larger or smaller? Can you derive it? (c) Consider the following statement: There is a 95% chance that / is smaller than 0.82. Is this statement correct? Explain your answer. (d) What is the confidence level for the interval , e [x - 2.3260/ vn, x + 2.3260/vn]