BTrue

Chebyshev’s inequality states that for any distribution, the proportion of values within $ k $ standard deviations from the mean is at least $ 1 - \frac{1}{k^2} $. For $ k = 2 $, this means at least $ 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = 0.75 $ or 75% of the values lie within 2 standard deviations of the mean.

In a normal distribution, approximately 95% of the values lie within 2 standard deviations of the mean. Therefore, Chebyshev’s inequality guarantees a minimum of 75%, which is less than the 95% for a normal distribution. Hence, the statement that 2 standard deviations from the mean will cover more values under Chebyshev’s inequality than under normal distribution is false.

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BTrue

Chebyshev’s inequality states that for any distribution, the proportion of values within $ k $ standard deviations from the mean is at least $ 1 - \frac{1}{k^2} $. For $ k = 2 $, this means at least $ 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = 0.75 $ or 75% of the values lie within 2 standard deviations of the mean.

In a normal distribution, approximately 95% of the values lie within 2 standard deviations of the mean. Therefore, Chebyshev’s inequality guarantees a minimum of 75%, which is less than the 95% for a normal distribution. Hence, the statement that 2 standard deviations from the mean will cover more values under Chebyshev’s inequality than under normal distribution is false.

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BTrue

Chebyshev’s inequality states that for any distribution, the proportion of values within $ k $ standard deviations from the mean is at least $ 1 - \frac{1}{k^2} $. For $ k = 2 $, this means at least $ 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = 0.75 $ or 75% of the values lie within 2 standard deviations of the mean.

In a normal distribution, approximately 95% of the values lie within 2 standard deviations of the mean. Therefore, Chebyshev’s inequality guarantees a minimum of 75%, which is less than the 95% for a normal distribution. Hence, the statement that 2 standard deviations from the mean will cover more values under Chebyshev’s inequality than under normal distribution is false.

Chebyshev’s inequality gives the proportion of values within k standard deviations around the mean for any shape of the distribution of values. Therefore, 2 standard deviations from the mean will cover more values under Chebyshev’s inequality than under normal distribution.AFalseBTrue

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