Question

Let X be a random variable with mean 6 and standard deviation 4. If L = 8-3X what is the standard deviation of L?

Answer 1

E(X ) = mean for x = 6

We calculate the variance of x by using the standard deviation of

Standard deviation (x) = 4

Formula

Var( a - b*X) = b² * Var(X)

Var(L) = 144

Now we find a standard deviation of L

Standard deviation of L = var(L)

$Standard \ deviation \ of \ L = \sqrt{144}$

$Standard \ deviation \ of \ L ={\color{Purple} \mathbf{12}}$

Another way

Standard deiation ( a - b*x ) = b * standard deviation (x)

Standard deviation of (L ) = standard deviation ( 8 - 3*x)

Standard deviation of (L ) = 3* Standard deviation (x)

We have standard deviation of (x) = 4

Standard deviation of (L ) = 3*4 = 12

Final answer:-

Standard deviation of (L ) = 12