The inspection of cans of juice involves sampling some cans and weighing them. The overall average for the samples is 39 ounces. Each sample contains 36 cans. The standard deviation is estimated to be 2 ounces. The 99.7% lower control chart limit for the average would be ________.
A) 37.67
B) 38.00
C) 39.33
D) 40.00
E) none

Question

Quizplus · Accepted Answer

The lower control limit for the average can be calculated as:
$\bar{x} - 3\frac{\sigma}{\sqrt{n}}$
where $\bar{x}$ is the sample average (39 ounces), $\sigma$ is the sample standard deviation (2 ounces), and $n$ is the sample size (36 cans).
Substituting in these values:
Lower control limit = 39 - 3(2 / $\sqrt{36}$) = 39 - 1 = 38
Therefore, the 99.7% lower control chart limit for the average would be 38 ounces, which corresponds to choice B.

The Inspection of Cans of Juice Involves Sampling Some Cans