Standard deviation?

If x has mean 5 and standard deviation 2, and y = 3 – 4x, what is the standard deviation of y?


a. standard deviation = -5


b. standard deviation = 5


c. standard deviation = -8


d. standard deviation = 8


e. cannot be determined from the given information


f. none of the above

Standard deviation?
Larry B has a good answer. My more visual approach would be to think of the y = 3 - 4x equation as stretching the curve by a factor of 4. Another way to look at this is that 1 unit in the first equation is being replaced by 4 units in the second equation. Since standard deviation can't be negative, the answer is 2 * 4 = 8 SD.
Reply:Think in terms of variances. Adding a constant has no effect on variance (or s.d.) so you can ignore the '3' term. The '-4x' is a linear term, which causes the variance to increase by a factor of (-4)^2 or 16. Now Var(x) is 2^2 or 4, so var(y) = 4*16 = 64, so s.d. of y = sqrt(64) = 8.
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