SOLUTION: Please show all of your work when answering the following: I. Use Chebyshev�s theorem to find what percent of the values will fall between 237 and 297 for a data set wit

Question 615720: Please show all of your work when answering the following:

I. Use Chebyshev�s theorem to find what percent of the values will fall between 237 and 297 for a data set with a mean of 267 and standard deviation of 15.

II. Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with a mean of 207 and standard deviation of 20.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 267
standard deviation is 15
score of 237 = z-score of (237-267)/15 = -2.0
score of 297 = z-score of (297-267)/15 = +2.0
k value = 2 standard deviations.
chebyshev states that the probability of scores being within this range will be greater than or equal to p = 1 - (1/k^2)
since k is equal to 2, this means that:
p = 1 - (1/4) which means that p = 3/4 which means that p = .75 or 75%.
this means that the probability that the scores will be between 237 and 297 is greater than or equal to 75%.
here's a reference that details how this calculation is made:
http://answers.yahoo.com/question/index?qid=20070914074905AAasH9q

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