Use the following table to answer the question(s) below.

-A machine shop owner wishes to monitor the diameter of an engine boring operation where the piston bore should be 4.25". He obtains 8 samples of 5 and records the data in the table above. What should the lower and upper control limits be for an X-bar chart?
A) (5.00, 8.00)
B) (-1.50, 1.50)
C) (4.33, 5.12)
D) (0.00, 1.45)
E) (-5.10, 5.10)

Question

Use the following table to answer the question(s) below.
 
-A machine shop owner wishes to monitor the diameter of an engine boring operation where the piston bore should be 4.25". He obtains 8 samples of 5 and records the data in the table above. What should the lower and upper control limits be for an X-bar chart?
A) (5.00, 8.00) 
B) (-1.50, 1.50) 
C) (4.33, 5.12) 
D) (0.00, 1.45) 
E) (-5.10, 5.10)

Quizplus · Accepted Answer

To find the control limits for an X-bar chart, we need to use the formula:

Upper Control Limit (UCL) = X-double-bar + A2*R-bar 
Lower Control Limit (LCL) = X-double-bar - A2*R-bar

where:
X-double-bar = average of all sample means
A2 = a constant from the standard normal distribution table based on the sample size (n=5 in this case), which is 0.577
R-bar = average range of the 8 samples, which is (0.08+0.04+0.08+0.08+0.08+0.08+0.04+0.08)/8 = 0.06

Plugging in the values, we get:

X-double-bar = (4.24+4.26+4.22+4.25+4.27+4.25+4.24+4.26)/8 = 4.245 
UCL = 4.245 + 0.577*0.06 = 4.303 
LCL = 4.245 - 0.577*0.06 = 4.187

Therefore, the lower and upper control limits for an X-bar chart are (4.187, 4.303), which is closest to option C.

Use the Following Table to Answer the Question(s) Below