Question: Let \({{X}_{1}},{{X}_{2}},....,{{X}_{10}}\) be ten observations of a certain normal random variable, with unknown mean and unknown variance. Suppose that the sample mean is 10.1 and the sample variance is \({{S}^{2}}\) is 0.0001

(a) Find the 95% confidence interval for the unknown mean

(b) Find the 95% prediction interval for the next observation (i.e. for \({{X}_{11}}\) )