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 23 centimeters (cm) and standard deviation 0.18 millimeters (mm). The length of a bearing has mean 2 cm and standard deviation 0.03 mm. What are the mean and standard deviation of the total length of the assembly? (Round your standard deviation answer to four decimal places.)

The mechanical assembly has three parts consisting of the length of the rod (the this be called x), the length of the bearing (be called y). You might be wondering where the third part is but the assembly usually has two bearings. Then the second length of the bearing (be called z).

From the problem,

μx = 23, μy =2, μz = 2

σx = 0.18, σy = 0.03, σz = 0.03

We can find the total Mean by adding all the means,

μxyz = 23 + 2 + 2 = 27cm

Since the length of the assembly are independent,

To find the total standard deviation, we must first find the total variance(square of standard deviation)

σ² = (0.18)² + (0.03)² + (0.03)² = 0.0342

Now, we find the standard deviation (square root of the variance)

σ = √0.0342 = 0.18493242

σ ≈ 0.1849mm (you can change to cm by multiplying by 10)