SOLUTION: The average value of a distribution is 150. If the standard deviation is 25, what percentage of the distribution lies within 100 and 200?

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Question 472559: The average value of a distribution is 150. If the standard deviation is 25, what percentage of the distribution lies within 100 and 200?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The distribution is not necessarily normal, so we use Chebyshev's inequality,
P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29+%3E=+1-1%2Fk%5E2. Since in this case, k = 2, we get

P%28abs%28X+-+150%29+%3C=+50%29+%3E=+1-1%2F4+=+3%2F4.
Hence at least 75% of the distribution lies with 100 and 200.
Note that if the distribution is normal, then by the empirical rule, around 95% would lie within 2 sd's of the mean, or between 100 and 200.