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?
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%.