Suppose that a random sample of eight observations is taken from the normal distribution with unknown mean μ and unknown variance σ2, and that the observed values are 3.1, 3.5, 2.6, 3.4, 3.8, 3.0, 2.9, and 2.2. Find the shortest confidence interval for μ with each of the following three confidence coefficients: (a) 0.90, (b) 0.95, and (c) 0.99.