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? 19.3 mm X B 20.6 mm 22.1 mm 23.5 mm E 24.9 mm
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? 19.3 mm X B 20.6 mm 22.1 mm 23.5 mm E 24.9 mm
Solution
The two-standard deviations rule for outliers states that any data point that falls more than two standard deviations away from the mean is considered an outlier.
Step 1: Calculate the range for non-outliers using the formula: [mean - 2*(standard deviation), mean + 2*(standard deviation)].
Step 2: Substitute the given values into the formula: [23.5 - 2*(1.4), 23.5 + 2*(1.4)] = [20.7, 26.3].
This means any thickness less than 20.7 mm or greater than 26.3 mm would be considered an outlier.
Step 3: Compare the given options with the calculated range.
The greatest thickness that would require the statistician to check the configuration of the machine is 24.9 mm, as it falls within the range of non-outliers (20.7 mm to 26.3 mm).
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