document.write( "Question 1178059: Suppose that the number of cars arriving in 1 hour at a busy intersection is a Poisson probability distribution with λ = 100. Find, using Chebyshev’s inequality, a lower bound for the probability that the number of cars arriving at the intersection in 1 hour is between 70 and 130.\r
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Algebra.Com's Answer #813753 by robertb(5830) $\"\"$ $\"About$

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For the Poisson distribution, $\"mu+=+100\"$ , and $\"sigma%5E2+=+100\"$ , and so $\"sigma+=+10\"$ .\r
\n" ); document.write( "\n" ); document.write( "Chebyshev's theorem says that $\"P%28abs%28X+-+mu%29%3C=+k%2Asigma%29+%3E=+1-1%2Fk%5E2\"$ .\r
\n" ); document.write( "\n" ); document.write( "==> $\"P%28abs%28X+-+100%29+%3C=+10k%29+%3E=+1-1%2Fk%5E2\"$ , and k has to be determined.\r
\n" ); document.write( "\n" ); document.write( " $\"abs%28X+-+100%29+%3C=+10k+\"$ is the same as $\"-10k+%3C=+X+-+100+%3C=+10k\"$ , or $\"70+=+100-10k+%3C=+X+%3C=+100%2B10k+=+130\"$ .\r
\n" ); document.write( "\n" ); document.write( "This implies that k = 3. We then get $\"P%28abs%28X+-+100%29+%3C=+30%29+%3E=+1-1%2F3%5E2+=+8%2F9\"$ .\r
\n" ); document.write( "\n" ); document.write( "Therefore a lower bound for probability of cars arriving at the intersection in 1 hour is between 70 and 130 is $\"highlight%288%2F9%29\"$ .\r
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