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.