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 upper control limit (UCL) for the mean?
A) 6.738
B) 6.999
C) 6.777
D) 7.221

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 upper control limit (UCL) for the mean?
A) 6.738 
B) 6.999 
C) 6.777 
D) 7.221

Quizplus · Accepted Answer

To calculate the upper control limit (UCL) for the mean, we need to use the formula:

UCL = X̄ + 3σ/√n

where X̄ is the sample mean, σ is the sample standard deviation, and n is the sample size.

From the given data, we have:

n = 6
X̄ = 6.75 (since the machine is calibrated to fill tubes of toothpaste at 6.75 ounces)
s = 0.096 (calculated using the standard deviation formula)

Plugging in these values into the UCL formula, we get:

UCL = 6.75 + 3(0.096)/√6
UCL ≈ 6.7766

Rounding this to three decimal places, we get the answer as C) 6.777.

A New Machine Is Set or Calibrated to Fill Tubes