In a metal fabrication process, metal rods are produced that have an average len

Question

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?

Select one:

a. This sample mean is only 1 standard deviation below the population mean.

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 2.38 standard deviations above what we expect.

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    19.5      
u = mean =    20.5      
n = sample size =    30      
s = standard deviation =    2.3      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -2.381402424      
          
Hence, as this is negative,

OPTION C: c. This sample mean is 2.38 standard deviations below what we expect. [ANSWER]

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