Question

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

• A. $144$
• B. $27$
• C. $12$
• D. $16$

Answer 1

The correct option is C $12$

If a random variable $X$ is adjusted by multiplying by the value $b$ and adding the value $a$, then the variance is affected as follows: ${\sigma }_{a+bX}^2=b^2{\sigma }^2$ , this is property of variance.
If the variance of the random variable X is 9; ${\sigma }^2$ = $9$
For random variable $-4X+8$
Variance = ${(-4)}^2{\sigma }^2=16\times 9=144$
Standard deviation = $\sigma =\sqrt{144}=12$