# About multiples of a SD

#### jhjahren

##### New Member
hey there, i have an issue with a task from my statistics book, its an introductory course in statistics for scientists (chemistry student), anyways the problem:

We have containers that should be filled with 0.55L each, the standard deviation from the machine error in filling is 0.07L. A box of these containers contain 12 of them, what is the standard deviation in volume of the entire box?

What i'm thinking here is that the variance is simply 0.07^2, and that the variance of a constant times a stochastic variable is the variance of the variable multiplied with the square of said constant. Which would mean that the standard deviation for the entire box should be sqrt(12^2 * 0.07^2). That answer is 0.84 but Maple TA (our electronic exercise system) doesn't accept the answer. I've just started statistics so i might be all wrong, anyone have some insight?

In advance, thanks #### CB

##### Super Moderator
I'm not great at this stuff, but I think the problem is that you're using the formula for the variance of a constant times a stochastic variable when you should just be looking for the variance of a sum of independent variates.

#### jhjahren

##### New Member
I'm not great at this stuff, but I think the problem is that you're using the formula for the variance of a constant times a stochastic variable when you should just be looking for the variance of a sum of independent variates.
As in sqrt( 0.07 * 12 ) as in the Variance of the box is the variance of each of the containers and thus the SD is the sqrt of that?

#### CB

##### Super Moderator
I think so, yes, though I think you mean sqrt(0.07^2 * 12) #### GretaGarbo

##### Human
We have containers that should be filled with 0.55L each, the standard deviation from the machine error in filling is 0.07L.
Is there anybody that have seen real data from an application like this? And would anybody believe that the error would be statistically independent?

And the filling machine has a standard deviation of 7 centiliter per bottle. So sometimes 14 cl to much or 14 cl to little (by empirical rule of Tjebychevs inequality)? That company has a problem! (Or maybe the teacher in formulating real homework problems.)