Individual parts combined to make a new one. Find mean and SD

[jafar]

Hi all,

I have found the mean and standard deviation of the length of a part using the probability density function I was given.

Density function of individual part is:

f_X (x)={ 10, 20.25<x<20.35
0, otherwise

Mean = 20.30 mm
Standard Deviation = 0.1/(sqrt12) mm

5 of these parts are then randomly chosen and put end-to-end to create a new combined part with length, W.

I need to find the mean and standard deviation of this new part??

I can only seem to find formulas for combining means and deviations of sample sizes, not for combining parts with the same mean and deviation.

Any help would be greatly appreciated.

[Dason]

I can only seem to find formulas for combining means and deviations of sample sizes, not for combining parts with the same mean and deviation.

What do you mean by this? Because I'm guessing you've found formulas for what you want to do but you're misunderstanding them.

[jafar]

I mean the pooling formulas for mean and standard deviation all use sample size n for each group. For instance:

To find the mean for two groups combined you use μ = (n1μ1 + n2μ2) / n, where n is the sample size of the groups. To find the standard deviation you would use SD = [ s₁(n₁ - 1) + s₂(n₂ - 1) ] / ( n₁ + n₂ - 2). However, I don't have a sample size for the individual parts so I'm not sure where to go from here.

[Dason]

Ah ok - so you found equations for pooling based on sample estimates.

http://en.wikipedia.org/wiki/Expected_value#Linearity
http://en.wikipedia.org/wiki/Standar...cal_properties

Since you're looking for the expectation and standard deviation of the sum of two independent random variables those links should help.