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
c 22.1 mm
d 23.5 mm
e 24.0 mm
incorrect
e
incorrect. this value is not an outlier based on the two - standard deviations rule for outliers. the value is only 1 standard deviation above the mean.

Explanation:

Step1: Recall outlier rule

For a normal - distribution, using the two - standard - deviations rule for outliers, outliers are values that are more than 2 standard deviations away from the mean.

Step2: Calculate the upper - bound non - outlier value

The mean $\mu = 23.5$ mm and the standard deviation $\sigma=1.4$ mm. The upper - bound non - outlier value is $\mu + 2\sigma$.
$\mu + 2\sigma=23.5+2\times1.4=23.5 + 2.8=26.3$ mm. The lower - bound non - outlier value is $\mu - 2\sigma=23.5-2\times1.4=23.5 - 2.8 = 20.7$ mm. We want the greatest value that would be an outlier (less than the lower - bound or greater than the upper - bound). Among the given options, values less than 20.7 mm are outliers.

Step3: Compare options

Option A: $19.3$ mm is less than $20.7$ mm. Option B: $20.6$ mm is less than $20.7$ mm. Option C: $22.1$ mm is greater than $20.7$ mm. Option D: $23.5$ mm is greater than $20.7$ mm. Option E: $24.0$ mm is greater than $20.7$ mm. The greatest value among the outliers (less than $20.7$ mm) is $20.6$ mm.

Answer:

B. $20.6$ mm