# Chebychev's theorem

1. Feb 14, 2006

### robasc

Could you please explain and break the steps down in solving the answer to this question for me?

In a distribution of 200 values, the mean is 50 and the standard deviation is 5. Use Chebychev's theorem.

a. at least what percentage of the values will fall between 10 and 30?

50 - 30 = 20

k = 20 / 5 = 4

1 - 1 / k^2 = 1 - 1 / 4^2 = 1 - 1 / 16 = .0625 = 1 - .0625 = .9375 or
%93.75

I got this part right but now this is the part I am having trouble with:

b. At least what percentage of the values will fall between 12 and 28?

Also, does at least mean to subtract?

2. Feb 15, 2006

### 0rthodontist

Chebychev's theorem states that at least 1 - 1/k^2 of the distribution lies within k standard deviations of the mean. Personally I don't see how you can use it here, maybe there's a trick. For part (a) your answer of 93% is the minimum percentage of values that fall between 30 and 70, not between 10 and 30.

Last edited: Feb 15, 2006
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