Floyd Electric is fabricating flanges for a new electrical motor. The flange is to be 25 millimeters in diameter with an upper tolerance limit of 26.5 millimeters and a lower tolerance limit of 23.5 millimeters. Bill Floyd took a sample consisting of ten flanges, measured the diameter and recorded the observations in the table. $$\begin{array} { | l | l | l | l | l | l | l | l | l | l }
25.69 & 25.58 & 24.78 & 24.94 & 24.87 & 24.63 & 25.70 & 25.52 & 24.95 & 24.91
\end{array}$$ What is Floyd Electric's process standard deviation?
A)0.15
B)0.17
C)0.42
D)0.39

Question

Floyd Electric is fabricating flanges for a new electrical motor. The flange is to be 25 millimeters in diameter with an upper tolerance limit of 26.5 millimeters and a lower tolerance limit of 23.5 millimeters. Bill Floyd took a sample consisting of ten flanges, measured the diameter and recorded the observations in the table. $$\begin{array} { | l | l | l | l | l | l | l | l | l | l } 
25.69 & 25.58 & 24.78 & 24.94 & 24.87 & 24.63 & 25.70 & 25.52 & 24.95 & 24.91
\end{array}$$ What is Floyd Electric's process standard deviation?
A)0.15
B)0.17
C)0.42
D)0.39

Quizplus · Accepted Answer

The formula to calculate the sample standard deviation is:

$s = \sqrt{\dfrac{\sum(x-\bar{x})^2}{n-1}}$

Using the given data, we have:

$\bar{x} = \dfrac{25.69+25.58+24.78+24.94+24.87+24.63+25.70+25.52+24.95+24.91}{10} = 25.12$

$s = \sqrt{\dfrac{(25.69-25.12)^2+(25.58-25.12)^2+(24.78-25.12)^2+(24.94-25.12)^2+(24.87-25.12)^2+(24.63-25.12)^2+(25.70-25.12)^2+(25.52-25.12)^2+(24.95-25.12)^2+(24.91-25.12)^2}{10-1}} = 0.42$

Therefore, the process standard deviation is 0.42 millimeters.