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?

Answer 1

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%.