Apply the Central Limit Theorem.
-In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. 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 feet and standard
Deviation of 0.42. 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 states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, typically n > 30, regardless of the population distribution. Here, the sample size is 30, and the mean and standard deviation of the sampling distribution are calculated using the population parameters, which aligns with the Central Limit Theorem.