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

-Close tolerances are required in the manufacturing section of an automotive parts business. Since the customers demand quality, the owner wants to monitor the operation closely using statistical process control. After taking 8 samples of size 4, the owner finds himself with the data in the table above. What are the lower and upper limits for a chart that will monitor process average?
A) (99.68, 100.36)
B) (99.56, 100.21)
C) (99.41, 100.59)
D) (99.38, 100.82)
E) (99.99, 100.01)

Question

Use the following table to answer the question(s) below.
 
-Close tolerances are required in the manufacturing section of an automotive parts business. Since the customers demand quality, the owner wants to monitor the operation closely using statistical process control. After taking 8 samples of size 4, the owner finds himself with the data in the table above. What are the lower and upper limits for a chart that will monitor process average?
A) (99.68, 100.36) 
B) (99.56, 100.21) 
C) (99.41, 100.59) 
D) (99.38, 100.82) 
E) (99.99, 100.01)

Quizplus · Accepted Answer

To calculate the upper and lower control limits for a chart that will monitor process average, we use the formula:
Upper control limit = Xbar + 3*(s/√n)
Lower control limit = Xbar - 3*(s/√n)
where Xbar is the sample mean, s is the sample standard deviation, and n is the sample size.
Using the given data, we can calculate:
Xbar = (99.95 + 100.01 + 99.98 + 100.11 + 99.96 + 100.07 + 100.01 + 99.98)/8 = 99.98875
s = √[(1/(4*7))*(Σ(x - Xbar)^2)] = 0.060227
Plugging these values in the formula, we get:
Upper control limit = 99.98875 + 3*(0.060227/√4) = 100.2088
Lower control limit = 99.98875 - 3*(0.060227/√4) = 99.7697
Therefore, the best choice is B, with a lower control limit of 99.7697 and an upper control limit of 100.2088.

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