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.
a. Describe the sampling distribution of the sample mean by naming the model and telling its mean and standard deviation.
b. Suppose the resulting sample mean is 19.5 metres. Do you think that this sample result is unusually small? Explain.

Question

Quizplus · Accepted Answer

The Answer is a. With a sample size of 30, the CLT says that the approximate sampling model for sample means will be the Normal model N(20.5, 0.42).
b. We have a random sample of metal rods drawn from a much larger population. A sample mean of only 19.5 metres is about 2.38 standard deviations below what we expect. The sample mean of 19.5 metres is unusually small.

In a Metal Fabrication Process, Metal Rods Are Produced That