Question

an auto transmission manufacturer receives ball bearings from two different suppliers. The ball bearings must have a specified diameter of 16.30 mm with a tolerance of +-0.1mm.Recent shipments from two suppliers had ball bearings with the following diameterssupplier A 16.23, 16.26, 16.31, 16.35, 16.37, 16.41,16.44Supplier B 16.19, 16.21, 16.26, 16.36, 16.38,16.42 16.45find the mean and standard deviation for the diameter of the ball bearings from supplier A

Answer 1

Solution

find the mean and standard deviation for the diameter of the ball bearings from supplier A​

For this case we need to remember the formulas for the mean and deviation given by:

$\text{Mean}=\frac{x_1+x_2+\text{.}\ldots+x_n}{n}=\frac{16.23+16.26+16.31+16.35+16.37+16.41+16.44}{7}=16.34$$\text{Variance}=\frac{(16.23-16.34)^2+(16.26-16.34)^2+(16.31-16.34)^2+(16.35-16.34)^2+(16.37-16.34)^2+(16.41-16.34)^2+(16.44-16.34)^2}{7-1}$

And we got:

Variance= 0.00588

And the deviation would be given by:

$\text{Devition}=\sqrt[]{0.00588}=0.0767$