\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(X\) be a random variable following the binomial distribution \(\mathcal{B}(45, 0.7)\) and let \(\alpha = 0.05\).
Determine the centered fluctuation interval \([a, b]\) at the threshold \(1 - \alpha\) associated with \(X\).
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