According to Chebyshev’s theorem, what proportion of a distribution will be with k=4 standard deviations of the mean? Show all work as to how to find this.
I have no idea on how to do this.
HELP!!!!
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To find the proportion of a distribution within a certain number of standard deviations from the mean using Chebyshev's theorem, you can follow these steps:
1. Determine the value of k, which represents the number of standard deviations from the mean.
In this case, k = 4 standard deviations.
2. Identify the proportion of the distribution within k standard deviations from the mean using Chebyshev's theorem formula:
The proportion of the distribution within k standard deviations from the mean is at least (1 - 1/k^2).
3. Substitute the value of k into the formula:
The proportion of the distribution within 4 standard deviations from the mean is at least (1 - 1/4^2).
4. Simplify the formula:
(1 - 1/4^2) = (1 - 1/16) = (15/16).
Therefore, according to Chebyshev's theorem, at least 15/16 or approximately 93.75% of the distribution will be within 4 standard deviations of the mean.
Remember that Chebyshev's theorem provides a lower bound, so the actual proportion within k standard deviations can sometimes be higher.