If $X$ is a normal random variable with a standard deviation of $10$, then $3X$ has a standard deviation equal to

Question

If $X$ is a normal random variable with a standard deviation of $10$, then $3X$ has a standard deviation equal to

A. $\sqrt {30}$

B. $90$

C. $30$

D. $10$

I choose $30$, but it is wrong, I also check Chegg, an answer from Chegg said answer should be A, but answer should be $3\cdot10=30$, why? My mistake or system error?

Answer 1

$Var(kX) = k^2Var(X)$

Thus is our case,

$\hspace{20mm} Var(3X) = 9Var(X) = 9*10^2 $
$\hspace{20mm} \sigma(3X) = \sqrt{9*10^2} = 3*10 = 30 $

So 30 should be the correct answer.