Apply Chebyshev's Theorem to find the least possible fraction of the numbers in a data set lying within $\frac{6}{5}$ standard deviations of the mean.
At least $\square$ of all numbers must lie within $\frac{6}{5}$ standard deviations from the mean.
(Type an integer or a simplified fraction)
Answer
Final Answer: The least possible fraction of the numbers in a data set lying within \(\frac{6}{5}\) standard deviations of the mean is approximately 0.3056 or \(\boxed{\frac{61}{200}}\) when simplified as a fraction.
Step 1 ：Chebyshev's theorem states that at least 1 - 1/k^2 of the data from a sample will fall within k standard deviations of the mean for all k > 1. In this case, k = \(\frac{6}{5}\).
Step 2 ：We need to calculate 1 - 1/(\(\frac{6}{5}\))^2 to find the least possible fraction of the numbers in a data set lying within \(\frac{6}{5}\) standard deviations of the mean.
Step 3 ：Final Answer: The least possible fraction of the numbers in a data set lying within \(\frac{6}{5}\) standard deviations of the mean is approximately 0.3056 or \(\boxed{\frac{61}{200}}\) when simplified as a fraction.
