SOLUTION: According to Chebyshev's theorem, 36% lie between ___ and ___ if mean is 42 and standard deviation is 12

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Question 1031032: According to Chebyshev's theorem, 36% lie between ___ and ___ if mean is 42 and standard deviation is 12
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Between 27 and 57.
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Chebyshev's Theorem says that P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29=+P%28abs%28X+-+42%29+%3C=+12k%29+%3E=+1-1%2Fk%5E2 for any distribution with mean mu and standard deviation sigma.
To find k, let 1+-+1%2Fk%5E2+=+0.36
==> 0.64+=+1%2Fk%5E2 ==> k%5E2+=+1%2F0.64 ==> k = 1.25.
==> abs%28X+-+42%29+%3C=+12%2A1.25 ==> abs%28X+-+42%29+%3C=+15
==> -15+%3C=+X+-+42+%3C=+15 ==> 27+%3C=+X+%3C=+57.