A new machine is set or calibrated to fill tubes of toothpaste at precisely 6.75 ounces. Then, once the machine is running, a sample of 6 tubes is taken every three hours and weighed with the following results: What is the lower control limit for the mean?
A) 6.738
B) 6.669
C) 6.699
D) 6.255

Question

A new machine is set or calibrated to fill tubes of toothpaste at precisely 6.75 ounces. Then, once the machine is running, a sample of 6 tubes is taken every three hours and weighed with the following results:  What is the lower control limit for the mean?
A) 6.738 
B) 6.669 
C) 6.699 
D) 6.255

Quizplus · Accepted Answer

The lower control limit for the mean can be calculated using the following formula: 
Lower control limit = Mean - (3 * Standard Deviation / sqrt(sample size))
Where, 
Mean = average weight of toothpaste tubes = (6.74+6.78+6.71+6.73+6.79+6.70)/6 = 6.7467
Standard Deviation = sqrt((sum of (xi - mean)^2) / (n-1)) = 0.03864
Sample size = 6
Plugging in the values, we get: 
Lower control limit = 6.7467 - (3 * 0.03864 / sqrt(6)) = 6.6986
Rounding off to three decimal places, we get the answer as 6.699, which is option C.

A New Machine Is Set or Calibrated to Fill Tubes