Consider the following to answer the question(s) below:
In a metal fabrication process, metal rods are produced that have an average length of 20.5 metres with a standard deviation of 2.3 metres. A quality control specialist collects a random sample of 30 rods and measures their lengths.
-The sampling distribution of the sample mean lengths is Normally distributed with a mean of 20.5 metres and standard deviation of 0.42 metres. We can say this because
A) The sample size is not too large.
B) The Central Limit theorem applies.
C) The Normal Probability theorem applies.
D) All of the above
E) None of the above

Question

Quizplus · Accepted Answer

The Central Limit Theorem applies when the sample is sufficiently large (n > 30) regardless of the underlying distribution of the population. This theorem states that the sampling distribution of the sample mean becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, choice B is the correct answer. Choice A is incorrect because the sample size is considered large enough. Choice C is not a known theorem, and Choice D is incorrect because not all choices are correct. Lastly, Choice E is incorrect because at least one option is the correct answer.

Consider the Following to Answer the Question(s) Below