Multiple choice

If the variance of the random variable X is $9,$ the S.D. of the random variable $-4X+8$ is:

  1. $144$
  2. $27$
  3. $12$
  4. $16$
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C Correct answer
Explanation

Variance of X is 9, so SD of X is 3. The SD of a*X + b is |a| * SD(X). Thus, SD of -4X + 8 is |-4| * 3 = 4 * 3 = 12.

AI explanation

Using the properties of variance, if Var(X) equals 9, then the variance of a linear transformation (-4X plus 8) is calculated by squaring the multiplier and multiplying it by the original variance. The calculation is (-4) squared multiplied by 9, which equals 16 multiplied by 9, giving a variance of 144. The standard deviation is the square root of the variance, so the square root of 144 is 12.

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