TABLE 8-2
A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.
-Referring to Table 8-2, the confidence interval is valid only if the lengths cut are normally distributed.

Question

Quizplus · Accepted Answer

The confidence interval is valid due to the Central Limit Theorem, which states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (typically n > 30), regardless of the population distribution.

TABLE 8-2 A Quality Control Engineer Is Interested in the Mean Length