Chebyshev's Theorem: percent between 120 & 150 for mu = 135

[maggiemagnet]

What is the percent of values that will fall between 120 and 150 for a data set with mean of 135 and standard deviation of 7.5 using Chebyshev's Theorem?

135 - 120 = 15 = 2 * 7.5

150 - 135 = 15 = 2 * 7.5

So I'm looking at k = 2 standard deviations. My understanding of Chebyshev's Theorem is that the percentage is "at least" 1 - (1/k^2). I get 1 - (1/4) = 1 - .25 = .75, or 75%. Is this correct?

The "empirical" rule says that about 95% are within two standard deviations (right?), so is this a contradiction of Chebyshev's Theorem, or is this where the "at least" comes into play?

Thank you.

[Martingale]

What is the percent of values that will fall between 120 and 150 for a data set with mean of 135 and standard deviation of 7.5 using Chebyshev's Theorem?

135 - 120 = 15 = 2 * 7.5

150 - 135 = 15 = 2 * 7.5

So I'm looking at k = 2 standard deviations. My understanding of Chebyshev's Theorem is that the percentage is "at least" 1 - (1/k^2). I get 1 - (1/4) = 1 - .25 = .75, or 75%. Is this correct?

yes

The "empirical" rule says that about 95% are within two standard deviations (right?), so is this a contradiction of Chebyshev's Theorem, or is this where the "at least" comes into play?

Thank you.

No it is not a contradiction. Chebyshev gives us a lower bound on the probability. If we are given more information about the underlying distribution (normality) then we can be more accurate with our probability calculation.

[maggiemagnet]

Thank you!