A higher order approximation formula for a percentage point of the noncentral t-distribution with \(\nu \) degrees of freedom is given up to the order \(o(\nu ^{-3})\) under the normality assumption, using the Cornish-Fisher expansion for the statistic based on a linear combination of a normal random variable and a chi-random variable. The upper confidence limit and the confidence interval for the noncentrality parameter are given. Although the approximation formula is represented as a solution of the equation, its existence and uniqueness are shown to be guaranteed. In a similar way to the above, without the normality assumption, a higher order approximation formula to a percentage point of the distribution of the noncentral t-statistic is also given. Further, a higher order approximation formula for a percentage point of the distribution of the sample correlation coefficient is given up to the order \(O(n^{-1})\) with a size n of sample. Numerical results are also given.