SOLUTION: Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, find the range in which at least 88.89% of the data will lie. Use Chebyshev's formula

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Question 465416: Americans spend an average of 3 hours per day online. If the standard deviation is 32 minutes, find the range in which at least 88.89% of the data will lie. Use Chebyshev's formula.
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Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Chebyshev's rule P%28abs%28X+-+mu%29+%3C=+k%2Asigma%29+%3E=+1+-+1%2Fk%5E2%29.
==>P%28abs%28X+-+180%29+%3C=+32k%29+%3E=+1+-+1%2Fk%5E2+=+0.8889%29.
Solving the equation 1+-+1%2Fk%5E2+=+0.8889%29, we get
1%2Fk%5E2+=+0.1111 ==> k%5E2+=+9 ==> k = 3.
==> P%28abs%28X+-+180%29+%3C=+32%2A3+=+96%29+%3E=+0.8889%29, or
the interval in question is
abs%28X+-+180%29+%3C=+96
<==> -96+%3C=+X+-+180+%3C=+96, or 84+%3C=+X+%3C=+276.