Question
A manufacturer of socks does a strength test of socks by stretching them until they tear. It is found that, socks within 3 standard deviations of the mean strength meet the standards. Using Chebychev’s theorem, what is the minimum percentage of the socks that meet the criteria?
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GPT 3.5
Chebyshev's theorem states that for any given dataset, the proportion of data points within k standard deviations of the mean is at least 1 - 1/k^2, where k is any number greater than 1.
In this case, the socks that meet the standards are those within 3 standard deviations of the mean strength. Therefore, k = 3.
Using Chebyshev's theorem, the minimum percentage of socks that meet the criteria is at least 1 - 1/3^2 = 1 - 1/9 = 8/9.
Therefore, the minimum percentage of socks that meet the criteria is at least 8/9 or approximately 88.89%.
In this case, the socks that meet the standards are those within 3 standard deviations of the mean strength. Therefore, k = 3.
Using Chebyshev's theorem, the minimum percentage of socks that meet the criteria is at least 1 - 1/3^2 = 1 - 1/9 = 8/9.
Therefore, the minimum percentage of socks that meet the criteria is at least 8/9 or approximately 88.89%.
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