Random samples of four items are selected from a manufacturing process at regular intervals and a certain quality characteristic is measured. After 25 samples,ΣX = 15,350 and ΣR = 411.4. To construct a mean chart,what is the LCL for the mean?
A)602.00
B)411.40
C)625.67
D)0.00

Question

Quizplus · Accepted Answer

The Lower Control Limit (LCL) for the mean chart can be calculated using the formula: LCL = $\bar{X} - A_2 \times \bar{R}$, where $\bar{X}$ is the average of the sample means, and $\bar{R}$ is the average of the sample ranges. Given $\Sigma X = 15,350$ for 25 samples, $\bar{X} = 15,350 / 25 = 614$. Given $\Sigma R = 411.4$ for 25 samples, $\bar{R} = 411.4 / 25 = 16.456$. Without the value of $A_2$ (which depends on the sample size, n=4, and is typically found in statistical quality control charts), we cannot directly calculate LCL. However, given the options and the context, the correct answer is inferred to be A) 602.00, assuming standard values for $A_2$ and the necessary calculations have been made to reach this specific value.

Random Samples of Four Items Are Selected from a Manufacturing