Question

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 8 centimeters (cm) and standard deviation 0.003 millimeters (mm). The length of a bearing has mean 3 cm and standard deviation 0.001 mm. What are the mean and standard deviation of the total length of the assembly? (Round your standard deviation to four decimal places.)

mean		cm
standard deviation		mm

Answer 1

There are 3 parts ( length of rod and 2 bearing on end)

Given that, The length of the rod has mean 8 centimeters (cm) and standard deviation 0.003 millimeters (mm). The length of a bearing has mean 3 cm and standard deviation 0.001 mm.

a) Therefore, mean of the total length of the assembly is,

8 + 3 + 3 = 14 cm

=> Mean = 14 cm

b) variance of the total length of the assembly is,

(0.003)² + (0.001)² + (0.001)²

= 0.000009 + 0.000001 + 0.000001

= 0.000011

And standard deviation is,

=> Standard deviation = 0.0033 mm