Let be a k-variate (k≧2) normal random vector with population mean vector and covariance matric ∑ of order k and let be the ordered values of the μ_i’s. No prior knowledge of the pairing of the μ[_i] with the X_j is assumed for any i and j . Based on a random sample of n vector observations of X, this paper considers both one-sided and a class of two-sided confidence intervals for μ[_k] and μ[₁] the largest and-the smallest component mean, respectively, when ∑ is equal to σ² R with common unknown variance sigma;²→0 and known correlation matrix R. An optimum two-sided coddence interval via finding the shortest length from this class is also considered. Necessary tables to actually apply these procedures are provided.