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Let \(X_1, X_2, \dots, X_{20}\) be independent random variables, each with mean \(\mu=174\) and standard deviation \(\sigma=4\).Let \(S_{20} = X_1 + X_2 + \dots + X_{20}\).
Find the mean of \(S_{20}\).
Find the variance of \(S_{20}\).
Find the standard deviation of \(S_{20}\).
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