Question

a statistician at a metal manufacturing plant is sampling the thickness of metal plates. if an outlier occurs within a particular sample, the statistician must check the configuration of the machine. the distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. based on the two - standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine? a 19.3 mm b 20.6 mm

Explanation:

Step1: Recall outlier rule

Outliers are outside $\mu\pm2\sigma$. We want upper - bound outlier.

Step2: Calculate upper - bound

$23.5 + 2\times1.4=23.5 + 2.8 = 26.3$. But we check options. For lower - bound $23.5-2\times1.4=23.5 - 2.8=20.7$. Option B ($20.6$ mm) is an outlier and is the greatest among outlier options.

Answer:

B. 20.6 mm