# Statistics Problem: Thickness of gears and spacers

1. Nov 16, 2005

### LakeMountD

A five-gear assembly is put together with spacers between the gears. The mean thicnkess of the gears is 5.03 cm with a standard ev. of .008. the mean thickness of the spacers is .140 cm with a standard dev. of .005. Find the mean and standard deviation of the thickness of the assembled units consisting of five randomly selected gears and four randomly selected spacers.

I am kind of confused on where to even start since I dont truly understand what the problem is asking.

2. Nov 17, 2005

### HallsofIvy

Staff Emeritus
Visualize the assembly! You have 5 gears with 4 spacers between them.
If you assume each gear is exactly 5.03 cm thick and each spacer is exactly 0.14 cm thick how thick would the whole assembly be?
Do you see how that's connected to the mean value of the thickness of the assembly?

To be more technical, if the probability density for the thickness of the gears is f(x) and the probability density for the thickness of the spacers is g(x) then the mean thickness of a gear is $\mu_1=\int xf(x)dx$ and the mean thickness of a spacer is $\mu_2=\int xg(x)dx$.
The mean thickness of a gear and a spacer together is $\int x(f(x)+g(x))dx= \mu_1+ \mu_2$.
The standard deviation of the thickness of the assembly is a little harder. Remember that standard deviation is defined in terms of "square root of a sum of squares".

Last edited: Nov 17, 2005