Use the Normal to Model the Distribution of Sample Means

Multiple Choice

Use the Normal to model the distribution of sample means.
-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. Suppose the resulting sample mean
Is 19.5 feet. Which of the following statements is true?

A) This sample mean is 2.38 standard deviations above what we expect.
B) This sample mean is more than 3 standard deviations away from the population mean.
C) This sample mean is 2.38 standard deviations below what we expect.
D) This sample mean is only 1 standard deviation above the population mean.
E) This sample mean is only 1 standard deviation below the population mean.