Instruction 8-3
A quality control engineer is interested in the mean length of timber poles being cut automatically by machine. The desired length of the insulation is 12 metres. It is known that the standard deviation in the cutting length is 0.15 metres. A sample of 70 cut poles yields a mean length of 12.14 metres. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.
-Referring to Instruction 8-3,the confidence interval is valid only if the lengths cut are normally distributed.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough, regardless of the shape of the population distribution. Since the sample size is 70, which is considered large (usually n > 30 is sufficient), the confidence interval can be considered valid without the need for the population to be normally distributed.

Instruction 8-3 A Quality Control Engineer Is Interested in the Mean Length