One piece of PVC pipe is to be inserted inside another piece

One piece of PVC pipe is to be inserted inside another piece identical PVC pipe. The length of this piece has a mean value 20 in. and standard deviation .5 in. The average length of overlap of those two pipes is 1.8 in. Also the standard deviation of the overlap is .3 in. What is the average total length of the assembly of the two pipes and what is its standard deviation?

Solution

Length of two pvc pipes = (20 + 20) inch = 40 inches

Length of overlap = 1.8 inches

Hence total length of assembly = (40 - 1.8) inch = 38.2 inches.

Variance of the assembly = 2 x 0.5² + .3² = 0.59 sq.inches

Standard deviation of the assembly = 0.768 inches.