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If a random variable x has standard deviation σ, then what is the standard deviation of the transformed variable (ax + b) / c, where a, b, and c are constants?

1. (a/c)σ
2. |a/c|σ
3. (a²/c²)σ
4. None of these

Correct answer: |a/c|σ

Solution

Adding a constant b shifts data without changing spread, while multiplying by a/c scales the SD by the absolute value. So SD((ax+b)/c) = |a/c|·sigma.

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