If the random variable \(X\) has mean 5 and standard deviation 4, then what is the standard deviation of the random variable \(Y = 3X + 4\)?
12
For \(Y=3X+4\), the standard deviation is scaled by the absolute value of the coefficient of \(X\), since adding a constant does not affect spread: \(\text{S.D.}(Y)=|3|\times\text{S.D.}(X)\). With \(\text{S.D.}(X)=4\), this gives \(\text{S.D.}(Y)=3\times4=12\).
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