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Chebyshev’s theorem guarantees that what proportion of a distribution will be included between the following: a. and b. and 2.148 According to Chebyshev’s theorem, what proportion of a distribution will be within k 4 standard deviations of the mean? 2.149 Chebyshev’s theorem can be stated in an equivalent form to that given on page 98. For example, to say “at least 75% of the data fall within 2 standard deviations of the mean” is equivalent to stating “at most, 25% x 2s x 2s x 3s x 3s (x 3s) (x 3s) will be more than 2 standard deviations away from the mean.” a. At most, what percentage of a distribution will be 3 or more standard deviations from the mean? b. At most, what percentage of a distribution will be 4 or more standard deviations from the mean?
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