Descriptive Statisticshard
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According to the Vysochanskij–Petunin inequality, for any unimodal and continuous distribution with mean μ\mu and standard deviation σ\sigma, the probability of an observation falling outside kk standard deviations from the mean is bounded by P(Xμkσ)49k2P(|X - \mu| \ge k\sigma) \le \frac{4}{9k^2} for k8/3k \ge \sqrt{8/3}. For a unimodal dataset of student test scores with mean μ=75\mu = 75 and standard deviation σ=6\sigma = 6, what is the maximum percentage of scores that can lie outside the interval [63,87][63, 87]?