Multiple choice

If the standard deviation of a variable x is 12, then the variance of the variable 2x + 17 is

  1. 24

  2. 288

  3. 576

  4. 41
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C Correct answer
Explanation

The variance of ax + b is a^2 * Var(x). Given standard deviation of x is 12, the variance of x is 12^2 = 144. Thus, the variance of 2x + 17 is 2^2 * 144 = 4 * 144 = 576.

AI explanation

The variance of the original variable x is the square of its standard deviation, which is 12 squared or 144. Using the property of variance, if a variable is transformed by multiplying by a constant k and adding a constant c, the new variance becomes k squared times the original variance. Here the variable is 2x + 17, so the new variance is 2 squared multiplied by 144, giving 4 times 144 which is 576.

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