A mechanical assembly consists of a rod with a bearing on each end. The three parts are manufactured independently, and all vary a bit from part to part. The length of the rod has...

A mechanical assembly consists of a rod with a bearing on each end. The three parts are manufactured independently, and all vary a bit from part to part. The length of the rod has mean 21 centimeters (cm) and standard deviation 0.003millimeters (mm). The length of a bearing has mean 2 cm and standard deviation 0.002 mm. What is the standard deviation of the total length of the assembly? (Round your standard deviation to four decimal places.)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The mechanical assembly consists of a rod with a bearing on each end. The three parts are manufactured independently, and all vary a bit from part to part. The length of the rod has mean 21 centimeters (cm) and standard deviation 0.003 millimeters (mm). The length of a bearing has mean 2 cm and standard deviation 0.002 mm.

To determine the standard deviation of the total length of the assembly, first the standard deviation of each of the components has to be squared. The resulting values are added and finally the square root of the sum is taken. This is the standard deviation of the length of the assembly. 

For the assembly described in the question, the standard deviation of the length is given by `sqrt(0.003^2 + 2*0.002^2)` = `sqrt(1.7*10^-5)` `~~ 4.1231*10^-3` mm.

The standard deviation of the length of the assembly is approximately `4.1231*10^-3` mm

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