2. Suppose you have a random sample of observations X1, ...,Xn of the number of seconds of advertisements shown before movie screenings at the cinema. You use the sample mean X to estimate the population mean u. (a) Suppose you know that the distribution of X1- is normal with known variance 02. Describe (using math) how to construct a 95% condence interval for u that is symmetric around X. (b) Now suppose 02 is unknown. Describe how to construct the same kind of 95% condence interval as in part (a) now. How does your condence interval differ when 02 is unknown. (c) Suppose now that you are unsure and are unwilling to assume that the distribution of the Xi is normal. How can you construct a symmetric 95% condence interval now? Is the interpretation any different than in parts (a) and (b)